11:06 p.m. Some excerpts from closing statements:
10:53 p.m. Trump said he "really" is ready to commit to not mounting a third-party bid, which he has threatened several times before.
"I've gained great respect for the Republican leadership...[and] the people on the dais," he said.
10:52 p.m. Cruz, in turn, is asked about his private comments questioning Trump's fitness to lead.
"People are looking for who is prepared to be a commander-in-chief," he said at a fundraiser recently, according to audio obtained by the New York Times. During his remarks about Trump and fellow GOP hopeful Ben Carson, the Texas senator asked: "Who understands the threats we face? Who am I comfortable having their finger on the button? Now that's a question of strength, but it's also a question of judgment. And I think that is a question that is a challenging question for both of them."
Pressed over whether Trump can be president, he said, "That is a judgment for every voter to make."
10:50 p.m. Trump is asked about the fact that he called Cruz a "maniac" over the weekend, even though he recently said he would be open to naming him as his running mate.
"I've gotten to know him over the last three or four days. He has a wonderful temperament. He's just fine," Trump said.
10:48 p.m. Trump skirts a question about his priority in upgrading the nuclear triad, the U.S. ability to launch nuclear bombs from B-52 bombers, from land, or from submarines. When pushed, he said he does not have a priority.
10:45 p.m. Christie's proposal to combat Chinese hacking: Get the most sensitive, embarrassing information and put it out in the public for the Chinese people to see.
Bush seconded Christie, saying the current administration has been too lax. He uses the answer to draw attention to Clinton's use of a private email server.
10:42 p.m. Fiorina fields a question about what she would do about North Korean leader Kim Jong Un, now that he claims to have a hydrogen bomb.
"We must continue to isolate him. We will need China as part of that strategy...one of the things we have to do if we want China's support is we have to push back on China. They too recognize one thing: Strength and their own economic interest," she said. She argued that the U.S. must push back on China's hacking and island-building in the South China Sea before asking for help dealing with North Korea.
Carson argues that economic power will help rebut U.S. enemies.
10:36 p.m. Christie points to the San Bernardino attacks to justify his opposition to letting refugees -- including orphans -- into the U.S.
"We now know from watching the san Bernardino attack that women can commit heinous, heinous acts against humanity," he said. "I don't back away from that statement, even for a minute."
10:34 p.m. Paul clarifies that he would not attempt to send home refugees who are already in the United States. But he also criticizes the fact that the government spends money to house and feed the ones who are here.
"We shouldn't have a program where we just say that we're going to take care of the world's refugees," he said.
10:31 p.m.Does Carson think refugee camps are a long-term solution to the problem of Syrian refugees?
"Their supreme desire is to be settled back in their own country," Carson said of his recent visit to the camps. He said that they wanted Americans to provide resources.
He argued that it would be possible to settle a lot of people in northern Syria as long as they are provided with weaponry.
10:26 p.m. Rubio plays the role of moderator for a minute, trying to nail down Cruz on whether he has ever supported allowing legalization for those who are in the country illegally.
"I never supported legalization and I do not intend to support legalization," he said.
"If we secure the border, that solves the problem," Cruz argued of illegal immigration.
10:22 p.m. Rubio defends his role in the 2013 Senate immigration bill that would have included a pathway to citizenship.
"Here's what we learned in 2013. The American people don't trust the federal government to enforce our immigration laws," he said. Before discussing citizenship, he said, the government would have to add more border agents, finish the border wall and implement an e-Verify system. At that point, he siad, "I think the American people are going to be very reasonable."
Cruz said Rubio chose to stand with President Obama and Sen. Chuck Schumer, D-New York, and chose "amnesty." He argued he stood with Sen. Jeff Sessions, R-Alabama, and the American people to oppose it.
10:17 p.m. Trump goes after the moderators for asking the other candidates about his words.
"The entire early portion of the debate was Trump this, Trump that...I think it's very unprofessional," he said.
Bush jumps in to say that if he finds the debate tough, he should imagine what it's like to deal with Putin.
10:13 p.m. Paul goes after Christie for saying he would shoot down a Russian plane in a Syrian no-fly zone.
"If you're in favor of World War III, you've got your candidate," he said.
He also references the Bridgegate scandal, saying that someone who would start World War III is the same kind of person who would shut down a bridge as an act of political retaliation -- what Christie aides were accused of doing in 2014.
10:12 p.m. Fiorina gets a question from a Facebook user about whether it is really feasible not to speak to Russian President Vladimir Putin, as she has said in the past she would.
"I didn't say I would cut off all communication with Putin, I said...now is not the time to talk to him," Fiorina said. "There is a time and a place for everything. There is a time and a place for talk, and there is a time and a place for action."
She said she would not talk to Putin until she had set up a no-fly zone in Syria, undone the Iran nuclear deal, rebuilt Sixth Fleet and reinstalled a missile defense system in Poland."
10:09 p.m. Paul says removing Assad would be "a huge mistake" and said that if the U.S. had bombed him in 2013 after he used chemical weapons, ISIS would have overrun the entire country of Syria.
10:07 p.m. Trump weighs in on the question of whether the U.S. should demand Assad's removal of power. As Hewitt puts it, that would mean that Iran and Hezbollah are "winning."
"I think Assad is a bad guy, a very bad guy," Trump said. But he argued that the U.S. needs to fight ISIS first and do one thing at a time. Only then can they consider whether Assad should stay.
10:03 p.m.: Carson gets the same question: Are Americans safer with dictators running the Middle East?
"No one is better off with dictators but there comes a time when you're on an airplane they always say in case of emergency oxygen masks will drop down, put yours on first...we need oxygen right now," he said, arguing that Americans need to help themselves before fixing other people's problems.
10:01 p.m. Fiorina responds to Trump's argument about having used money from the Middle East at home.
"That's exactly what President Obama has said. I'm amazed to hear that from a Republican presidential candidate," she said. Then she pivoted to Clinton, saying, "Hillary Clinton has gotten every foreign policy challenge wrong."
9:59 p.m. Candidates argue over whether Syrian dictator Bashar Assad needs to go. Cruz warned that there are no moderate rebels to take his place. Rubio argues he funds terrorists like Hezbollah. Kasich also argues that he must go.
Trump is briefly interrupted by a protester in the debate hall. Then he argues that if the money spent toppling dictators in the Middle East had been used to repair roads in the U.S., "we would have been a lot better off."
"The Middle East is totally destabilized," he said.
9:57 p.m. Cruz blames some Republicans in Congress as well as President Obama and former Secretary of State Hillary Clinton for supporting toppling dictators like Muammar Qaddafi in Libya and Hosni Mubarak in Egypt. He argued it led to chaos.
Rubio defended his support of airstrikes to depose Quaddafi, arguing he had American blood on his hands.
9:50 p.m. On foreign policy, Fiorina quotes former British Prime Minister Margaret Thatcher.
"Margaret Thatcher once said, 'If you want something talked about. If you want something done, ask a woman,'" she said.
Christie, asked about his strategy to fight ISIS, criticizes the politicians on stage who he says are complaining about the degrading of the U.S. military even though they voted in favor of the mandatory budget cuts implemented in a 2011 budget deal (sequestration).
9:47 p.m. Blitzer presses Rubio about how he would get Sunni troops to fight ISIS on the ground when they have conducted less than 5 percent of airstrikes against the group, and none since August.
"They most certainly will be have to worked on to provide more than they are doing right now," he said. Rubio argued the reason they have not participated more is that, "they have lost complete trust and confidence in this president. This president cut a deal with their mortal enemy, the Shia, in Iran," he said, referring to the Iran nuclear deal.
9:43 p.m. Paul goes after Trump for his proposal to kill the families of terror suspects, saying it goes against the Constitution.
"They can kill us, but we can't kill them?" Trump says, arguing that's what Paul is saying.
When the audience boos, Trump says, "These are people who want to kill us folks. And you're objecting to us infiltrating their conversation? I don't think so."
9:42 p.m. Carson has a back and forth with moderator Hugh Hewitt, who asked whether he would be able to order airstrikes that would kill thousands of children.
Carson likened it to telling a child he needs to open up his brain to take out a tumor.
"Later on they really realize what's going on and by the same token you have to be able to look at the big picture and understand that it's actually merciful if you go ahead and finish the job rather than death by 1,000 pricks" he said.
"Can you be as ruthless as Churchill was?" Hewitt asked.
"Ruthless is not necessarily the word I would use but tough, resolute, understanding what the problems are and understanding that the job of the president of the United States is to protect the people of this country," he responded.
9:40 p.m. Bush is determined not to let Trump have the last word.
"Donald, you're not going to be able to insult your way to the presidency. That's not going to happen. And I do have the strength...leadership is not about attacking people and disparaging people, leadership is about creating a serious strategy to deal with the threat of our time," he said.
"With Jeb's attitude, we will never be great again," Trump responded.
9:37 p.m. A questioner from Facebook asks Trump how his suggestion to kill the families of ISIS members makes the U.S. any different from the group, because the proposal fails to distinguish between combatants and civilians.
"We have to be much tougher, we have to be much stronger than we've been," he said, arguing that family members know about terrorism. "They may not care much about their lives but they do care, believe it or not, about their families' lives."
Bush cuts in, saying that was another example of a non-serious proposal from Trump. Then the two proceed to talk over each other.
"I know you're trying to build up your energy, Jeb, but it's not working," Trump said.
9:35 p.m. Cruz hits back at Rubio.
"ISIS and radical Islamic terrorism will face no more determined foe than I will be, we will utterly destroy them by targeting the bad guys and one of the problems with Marco's foreign policy is that he's all too often supported Hillary Clinton and Barack Obama undermining dictators in the Middle East that have aided radical Islamic terrorism," Cruz said.
9:33 p.m. A difference between Cruz and Rubio emerges, as Rubio criticizes Cruz for a heavy focus on bombing ISIS.
"ISIS Is a radical Sunni group. They cannot just be defeated through airstrikes," he said.
He also calls for better anti-ISIS propaganda that shows what life is really like under the group.
9:31 p.m. "Political correctness is killing people," Cruz said. He said that was the reason the Obama administration didn't stop Tashfeen Malik, the female attacker in the San Bernardino shooting, from entering the U.S. -- because they didn't look at her Facebook account and see public declarations of support for ISIS.
9:28 p.m. Kasich has been pressing hard on the problem of encrypted communications, saying local authorities need more ability to penetrate communications.
9:27 p.m. Trump says he would be "open" to closing parts of the internet where the U.S. is fighting with people.
9:26 p.m. Fiorina initially dodges a question on whether private sector companies should be forced to give the government access to encrypted communications.
"We were using the wrong algorithms," she said of missing people like the Boston marathon bombers and the couple who carried out the shooting in San Bernardino. "This is a place where the private sector could be helpful."
Pressed on whether Silicon Valley companies should be forced to cooperate, she says, "They do not need to be forced. They need to be asked, to bring the best and brightest."
9:21 p.m. Carson is the first candidate to complain about time when he gets a question about his proposal to monitor some mosques and schools.
"It's the first time I've spoken and several people have had multiple questions so please try to pay attention to that," he told moderators.
"My point is we need to make sure that any place, I don't care whether it's a mosque, a school...if there are a lot of people engaging there in radicalizing activities, then we need to be suspicious of it, we need to get rid of all this P.C. stuff," he said.
Asked who was right in the debate between Rubio and Paul over surveillance, Carson said he wanted to stay out of it.
9:19 p.m. Christie said the debate over legislation makes his eyes glaze over and goes after his Senate colleague, saying, they are "people who have never had to make a consequential decision in an executive position."
9:17 p.m. Paul goes after Rubio not for surveillance -- the issue where they disagree significantly -- but for his stance on immigration.
"Marco has opposed at every point increased border security for those who come to our country," Paul said. "He's the weakest of all the candidates on immigration."
Rubio pushes back, again defending increased surveillance.
"I bet you we wish we would have had access to five years of his records," he said of Syed Farook, the San Bernardino shooter who was an American citizen.
9:15 p.m. Rubio criticizes Cruz's vote on the USA Freedom Act, saying it took a tool away from the government. Cruz accuses him of lying about what the bill does.
"What he knows is that the old program covered 20 to 30 percent of phone numbers to search for terrorists, the new program covers nearly 100 percent," Cruz said.
9:13 p.m. Cruz defends his vote in favor of the USA Freedom Act, which ended the National Security Agency (NSA) collection of bulk phone records.
In addition to reforming surveillance, "it strengthened the tools of national security and law enforcement to go after terrorists," he said.
9:08 p.m. Fiorina argues the private sector must do more to help the government stop terrorism from unfolding in the tech sphere. She cited some of her own experiences.
"Soon after 9/11 I got a phone call from the NSA. They said they needed help. I gave them help...we need the private sector's help because the government is not innovating," she said.
9:06 p.m. Cruz is also asked to respond specifically to why he opposes Trump's plan.
"Everyone understands why Donald has suggested what he has. We're looking at a president who has engaged in this doublespeak where he doesn't call radical Islamic terrorism by its name," he said.
He said the legislation he introduced in Congress -- suspend for three years refugees from countries where terrorism has a strong presence -- is more narrowly focused than Trump's proposal.
9:04 p.m. Asked about polling that shows a majority of Republicans support Trump's ban on Muslims, Rubio said, "I understand why they feel that way, because this president hasn't kept us safe...this is what's important to do: we must deal frontally with this threat of radical Islamists, especially ISIS."
9:01: Bush explains why he objects to Trump's plan: if we are going to ban all Muslims how are we going to get them to be part of a coalition to destroy ISIS?"
"Donald is great at the one liners, but he is a chaos candidate and he would be a chaos president," he said.
"Jeb doesn't really believe I am unhinged, he said that very simply because he has been a disaster in his campaign," Trump responded.
9:00 p.m. First question goes to Trump, who is asked about his plan to temporarily ban all Muslims from entering the U.S.
"We're talking about security, we're not talking about religion, we're talking about security," he said.
8:46 p.m. Some excerpts from the candidates' opening statements:
Paul: "The question is, how do we keep America safe from terrorism? Trump says we ought to close that internet thing. The question is what does he really mean by that....Rubio says we should collect all Americans' records all the time. The Constitution says otherwise...I think we defeat terrorism by showing them we do not fear them.
"If we want to defeat terrorism, we need to quit arming the allies of ISIS."
Kasich: "When we think about our country and the big issues, Wolf, that we face in this country - creating jobs, making sure people can keep their jobs...these are all the things that we need to focus on but we'll never get there if we're divided. We'll never get there if Democrats and Republicans just fight with each other...I believe we need to unify in so many ways to rebuild our country."
Christie: "America has been betrayed. We've been betrayed by the leadership that Barack Obama and Hillary Clinton have provided to this country over the last number of years...the second largest school district in America closed based on a threat. Think about the effect that's going to have on those children when they go back to school tomorrow...I'm a formal federal prosecutor, I've fought terrorists and won and when we get in the White House we will fight terrorists and win again."
Fiorina: "Like all of you, I'm angry, I'm angry at what's happening to our nation. Citizens, its time to take our country back. Bombast and insults wont' take it back. Political rhetoric that promises a lot and delivers a little won't take it back. All of our problems can be solved, all of our wounds can be healed by a tested leader who is willing to fight for the character of our nation. I have been tested. I've beaten breast cancer. I've buried a child...I've made it to the top of corporate America while being called every b-word in the book."
Bush: "Our freedom is under attack. Our economy us under water...America is under the gun...serious times requires strong leadership, that's what's at stake right now. Regarding national security we need to restore the defense cuts of Barack Obama."
Rubio: "There have always been people in the world who wanted America to be more like the rest of the world...millions of Americans feel out of place...around the world America's influence has declined. While this president has destroyed our military, our allies no longer trust us and our adversaries no longer respect us...if you elect me president you will have a president who believes America is the greatest country in the world and we will have a president who acts like it.
Cruz: "Our enemy is not benevolent extremism...it is radical Islamic terrorism...every one of us is better prepared to keep this nation safe than is Barack Obama or Hillary Clinton. We need a president who understands the first obligation of the commander-in-chief is to keep America safe. If I am elected president, we will hunt down and kill the terrorists."
Carson: Started by calling for a moment of silence for the victims of the San Bernardino shooting. "Right now, the United States of America is the patient and the patient will not be cured by political correctness and will not be cured by timidity."
Trump: "I began this journey six months ago. My total focus was on building up our military, building up our strength, building up our borders, making sure that China, Japan, Mexico, both at the border and in trade no longer takes advantage of our country. Certainly would never have made that horrible disgusting absolutely incompetent deal with Iran...A month ago things changed. Radical Islamic terrorism came into effect...people like what I say, people respect what I say and we've opened up a very big discussion that needed to be opened up.
8:35 p.m. Nine candidates are about to take the stage for the fifth Republican debate in Las Vegas: Businessman Donald Trump, former neurosurgeon Ben Carson, Florida Sen. Marco Rubio, Texas Sen. Ted Cruz, former Florida Gov. Jeb Bush, former Hewlett-Packard CEO Carly Fiorina, Ohio Gov. John Kasich, New Jersey Gov. Chris Christie and Kentucky Sen. Rand Paul. Trump will be at center stage, Carson will be standing on his right, and Cruz will be on his left.
Christie is returning to the main debate stage after being relegated to the lower tier for the Fox Business debate, and Paul narrowly escaped the undercard for this debate, when Fox News released a poll that showed him with 5 percent support in Iowa. The threshold for the candidates was an average of 3.5 percent national support or 4 percent in either New Hampshire or Iowa, and although Paul didn't meet that, a CNN spokesperson said, "In the light of new polling released this morning and in the spirit of being as inclusive as possible, CNN has decided to include Sen. Rand Paul in the prime-time debate."
Earlier Tuesday evening, four other candidates competed in the undercard debate: former Arkansas Gov. Mike Huckabee, South Carolina Sen. Lindsey Graham, former Pennsylvania Sen. Rick Santorum and former New York Gov. George Pataki. You can read the CBS News liveblog of that debate here.
The debate is being moderated by CNN Lead Political Anchor Wolf Blitzer, CNN Chief Political Correspondent Dana Bash and Salem Radio Network talk show host Hugh Hewitt will moderate the debate.
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