Last Updated Jan 15, 2016 1:54 AM EST
11:21 p.m. After the last-minute fireworks from Cruz and Rubio, the candidates are wrapping up with closing statements.
11:11 p.m. Cruz went after Rubio for not supporting border security, prompting Rubio to accuse him of flip-flopping on issues ranging from immigration to national security to the military budget.
"That is not consistent conservatism," Rubio said. "That is political calculation."
Cruz responded, "I appreciate you dumping your oppo research folder on the debate...at least half of the things Marco said are flat-out false."
11:07 p.m. Asked about the Senate immigration bill he helped write allowing more immigrants to come to the country legally when American workers need jobs, Rubio pivoted to talking about the need to tighten security for all immigrants.
"The issue is dramatically different than it was 24 months ago," he said.
11:04 p.m. Kasich was asked to weigh in on a new training program for Chicago police. He talks about ways that Ohio is doing police retraining, but also said one of the key issues is ""integration of community and police."
"As president of the United States, it's all about communication, folks. It's all about getting people to listen to one another's problems," he said.
11:00 p.m. Would Trump put his assets into a blind trust if he's elected?
"It's an interesting question because I'm very proud of my company...but if I become president I couldn't care less about my company," he said.
He then gestured to his children in the audience.
"Run the company kids, have a good time. I'm going to do it for America," he said.
10:53 p.m. Rubio hits back by arguing that Cruz can't eliminate the IRS as he is promising to do, because "someone has to be there to collect your VAT tax." He also argues that companies will pay employees less and charge companies more.
10:53 p.m.Rubio said that unlike Cruz, he would not implement a value-added tax (VAT) because it obscures the true cost of government. Cruz responds that a business flat tax is not a value-added tax, and it also allows the U.S. to eliminate other taxes such as the estate tax and payroll taxes.
10:47 p.m. Asked about how to fix America's roads and bridges without "breaking the bank," Christie argues for reforming the tax code to bring the corporate tax rate down to 25 percent and allow for a one-time repatriation of overseas profits at just an 8.75 percent rate.
Carson argued for getting rid of regulations and implementing a flat tax.
10:40 p.m. In a rare moment, Cruz plays the conciliator and says both Trump and Bush are right on the issue.
He pushes his tax plan, which he said would make every export tax free and every import would pay a business flat tax.
10:38 p.m. Bush looks for a few early-state votes by warning that China would retaliate against tariffs -- possibly by blocking soybeans from Iowa.
"We need someone with a steady hand as president of the United States," he said. Trump responds, "We don't need a weak person being president of the United States, because that what we'll get if we have Jeb."
10:36 p.m. "You have to be careful with tariffs," Rubio warns, saying they get passed onto the buyer. He said the best way to protect the U.S. from China is to grow the economy. Trump said that method will take too long.
When the moderators ask whether Rubio is right about the tariff getting passed onto consumers, Trump insisted "it will never happen" because China will let their currency rise.
10:32 p.m. Trump has a back and forth with Cavuto about whether he would impose a 45 percent tariff on Chinese goods, which he has suggested before.
"I'm saying absolutely, we don't have to continue to lose $505 billion as a trade deficit for the privilege of dealing with China. I'm a free trader. I believe it. But we have to be smart."
"You're open to a tariff?" Cavuto asked.
"I'm totally open to a tariff if they don't treat us fairly," he said.
10:25 p.m. Other candidates are asked whether they would pause Muslim immigration.
Kasich: "I've been for pausing on admitting the Syrian refugees...I don't believe we have a good process on being able to vet them. But you know we don't want to put everybody in the same category," he said. He also talked about the need to build a coalition with Muslim countries.
Christie: "I said right from the beginning we should take no Syrian refugees of any kind...after spending seven years as a former federal prosecutor, right after 9/11 dealing with this issue...you can't just ban all Muslims. You have to ban radical Muslim jihadists." He said the intelligence community needs more funding and tools and criticizes those who tried to restrict spying by the National Security Agency.
Rubio: "If we do not know who you are, and we do not know why you are coming...you are not getting into the United States of America."
Cruz: "I understand why Donald made the comments he did and I understand why Americans are feeling scared and frustrated," he said. He urged Congress to pass a bill stripping Americans of citizenship if they go to fight with ISIS, and also pass legislation stopping all refugees from countries controlled by ISIS or al Qaeda.
Carson: "Clearly what we need to do is get a group of experts together, including people from other countries...come up with some new guidelines for immigration and for visas for people who are coming into this country."
Bush: "What we need to do is destroy ISIS." He said the U.S. will not ban Muslims from places like Indonesia. "You don't solve [the problem] by big talk about banning all Muslims."
10:23 p.m. Bush is asked about his comments calling Trump "unhinged" after making the proposal. Cavuto asked: Are the people who agree with Trump unhinged?
"No," Bush said. "I can see why people are angry and scared...I totally get that. But we are running for the presidency of the United States here. This is a different kind of job. You have to lead. You can't make rash statements."
10:21 p.m. Bush asks Trump to reconsider.
"This policy is a policy that makes it impossible to build the coalition that is necessary to take out ISIS," he said.
10:19: Bartiromo notes that more than 10 million people have discussed Trump's proposal to temporarily ban Muslims from the U.S. after the San Bernardino shootings. Was there anything he heard, she wanted to know, that makes him want to rethink the position?
"No," Trump responds.
10:16 p.m. South Carolina Sen. Lindsey Graham dropped out of the Republican presidential race, but the candidates are still getting questions about his proposals to fight against the Islamic State of Iraq and Syria (ISIS) such as sending 20,000 troops to fight the group.
Carson advocated for listening more to the generals and being more aggressive about bombing targets like oil tankers controlled by ISIS.
On whether Syrian President Bashar Assad must go, Christie said, "You're not going to have peace in Syria with Assad in charge. You're simply not. So Sen. Graham is right about this."
10:08 p.m. Though much of the focus on foreign policy has been about the threat from Iran, Cavuto asked Kasich what he makes of recent events in Saudi Arabia. Tensions between the U.S. Sunni ally and Iran are high after Saudi Arabia executed a prominent Shia cleric.
"My biggest problem with them is that they're funding radical clerics," Kasich said. "Whether I'm president or not we better make it clear to the Saudis that we're going to support you...but you've got to knock off the funding and teaching of radical clerics."
10:05 p.m. A tough moment for Cruz after he is asked what he means when he talks about "New York values."
"The values in New York City are socially liberal...focused around money and the media," he said.
Trump comes back at him by invoking the 9/11 attacks. "When the world trade center came down I saw something that no place on earth could have handled more beautifully, more humanely than New York," he said.
10:01 p.m. Cruz argues that all candidates in a GOP primary are going to pledge to protect the Second Amendment, but voters are "savvier" than that.
"They recognize that people's actions don't always match their words. I've got a proven record fighting to protect the Second Amendment," he said. "The other individuals on this stage wouldn't know where to be found in that fight."
9:59 p.m. In a particularly impassioned moment, Christie promises the president Republicans will "kick your rear end of the White House" in fall.
9:55 p.m. Rubio piles on as well.
"I am convinced that if this president could confiscate every gun in America, he would," Rubio said.
He also criticized Mr. Obama's recent executive actions to reduce gun violence, saying that criminals don't procure guns through methods that would subject them to a background check.
Moderator Neil Cavuto presses Rubio about whether that's an extreme position, but Rubio doubles down and references Mr. Obama's comment about people clinging to guns and religion during the 2008 campaign.
9:53 p.m. Bush is asked about gun control in the context of the Charleston, South Carolina shooting earlier this year.
"The law itself requires a background check but they didn't fill their end of the bargain...we don't need to add new rules, we need to make sure the FBI does their job," he said.
Trump also said he opposes any restrictions on guns, and echoed Bush in urging a focus on mental health.
9:46 p.m. Carson gets the question about whether former President Bill Clinton's sexual history is fair game. The audience seemed to think it was, with several yelling "yes." And it's been a frequent topic on the campaign trail, particularly from Trump.
"There's no question we should be able to look at any past president whether they're married to someone who's running for president or not," he said, before shifting to a larger question about morality.
"Here's the real issue: Is this America anymore? Do we still have standards? Do we still have values and principles?" he said.
He said some people still recognize what is "right and wrong" but that they should not let "secular progressives" drive that out.
9:40 p.m. Rubio and Christie tussle over whether Christie's policies are liberal.
"We cannot afford to have a president of the United States who supports Common Core," he said, and also questioned Christie's record judicial nominees and abortion access."
Christie fires back at Rubio's points and also makes an oft-repeated argument that while senators talk, governors act.
"You're held accountable for everything that you do," he said. "I like Marco too and two years ago he called me a conservative reformer that new jersey needed. That was before he was running against me. Now he's changed his tune. I'm never going to change my tune."
9:37 p.m. Trump got a question about how he would unite the GOP after South Carolina Gov. Nikki Haley, who delivered the official Republican response to President Obama's State of the Union address, urged members of her own party to resist the temptation to follow the "siren call of the angriest voices."
"I will gladly accept the mantle of anger," Trump said, because the people running the country are "incompetent."
9:31 p.m. Cruz finally gets the question about Trump's attacks on his citizenship, and accuses Trump of attacking him because his poll numbers have risen in Iowa.
"Back in september my friend Donald said he had had his lawyers look at it from every which way and there was nothing there, there was nothing to this birther issue..since September the Constitution hasn't changed. But the poll numbers have. And I recognize, I recognize that Donald is dismayed that his poll numbers are falling in Iowa. But the facts and the law here are really quite clear here. Under longstanding U.S. law the child of a U.S. citizen born abroad is a natural born citizen," he said.
Cruz went on to note that some of the more "extreme" birther theorists say that a natural born citizen must have two parents born in the United States, which would also disqualify Trump from the presidency.
"I'm not going to use your mother's birth against you. You are an American as is everybody else on this stage and I would suggest we focus on who is best prepared to be commander in chief because that's the most important question facing the country," Cruz said.
Trump once again told Cruz he should seek a declaratory judgment that he is eligible to run, because if Cruz was his vice presidential nominee -- or the nominee himself -- Democrats would challenge his citizenship.
He also admitted he's raised the issue, "because now he's doing a little bit better."
"I didn't care before," Trump said. But now, "He's got probably a 4 or 5 percent chance."
Cruz's response to Trump: "I'm happy to consider naming you as VP so if you happen to be right you can get the top job at the end of the day."
"I think I'll go back to building buildings," Trump responded.
9:22 p.m. When about the New York Times that he failed to disclose a low-interest loan from his wife's employer, Goldman Sachs, Cruz begins by railing about the what he viewed as a "hit piece." Then he talked about his struggle as the underdog in the 2012 Texas Senate campaign.
"Yes I made a paperwork error...but if that's the best hit the New York Times has got they've better go back to the well," Cruz said.
9:20 p.m. In his first answer of the night, Trump warns that migrants could be the "great Trojan horse" of attacks on the U.S. and said he is skeptical there are few women coming to the U.S.
9:16 p.m. Guantanamo Bay would definitely remain open under a President Rubio. He promised that any terror suspects captured abroad would get a "one-way ticket" to the Cuban prison facility.
9:14 p.m. As the debate turns to foreign policy, both Christie and Bush say the military has become weak under Mr. Obama and needs to be strengthened. Both also warn that Democratic candidate Hillary Clinton would be a disaster as president because she would continue the president's foreign policies.
Rubio also chimes in.
"Hillary Clinton is disqualified from being commander in chief of the United States. Someone who cannot handle intelligence information appropriately cannot be president of the United States," he said, in a reference to Clinton's email use as secretary of state.
9:06 p.m. The first question goes to Texas Sen. Ted Cruz, who is asked about President Obama's assessment of the economy in his State of the Union address. Instead, he opted to first talk about the sailors who were captured by Iran and then released earlier this week.
"In that State of the Union President Obama didn't so much as mention the 10 sailors that had been captured by Iran. President Obama is preparing to send $100 billion or more to the Ayatollah Khomeini," Cruz said. "The next commander in chief is standing on this stage....no serviceman or servicewomen will be forced to be on their knees.
8:57 p.m.: Just seven candidates are taking the stage for the sixth Republican debate in North Charleston, South Carolina: businessman Donald Trump, Texas Sen. Ted Cruz, Florida Sen. Marco Rubio, neurosurgeon Ben Carson, New Jersey Gov. Chris Christie, former Florida Gov. Jeb Bush and Ohio Gov. John Kasich.
Fox Business Network, which is hosting the debate, raised the bar for entry in the main debate. Canddiates had to place among the top six candidates nationally in an average of the five most recent national polls recognized by Fox News, or in the top five in either Iowa or New Hampshire, based on recognized polls in those states.
Earlier in the evening, former Hewlett Packard CEO Carly Fiorina, former Pennsylvanian Sen. Rick Santorum and former Arkansas Gov. Mike Huckabee participated in the undercard debate. Sen. Rand Paul, R-Kentucky, is boycotting the lower-tier debate after he was deemed ineligible for the main stage. Fox Business rejected Paul's appeal Wednesday to participate in the first-tier debate.
The debate is being moderated by Neil Cavuto, a Fox Business Network anchor and managing editor of business news, and anchor Maria Bartiromo.