Speaking in the spin room after the Fox Business GOP debate on Jan. 14, Donald Trump continued his attacks against Ted Cruz. (Dalton Bennett/The Washington Post)

The mutually beneficial campaign detente between Donald Trump and Sen. Ted Cruz (Tex.) came to an end on the debate stage here Thursday.

The two Republican presidential candidates, locked in a tight race to win the Feb. 1 Iowa caucuses, argued over whether Cruz meets the constitutional requirements to serve as president and whether Trump is a trustworthy conservative or is tainted by what Cruz called “New York values.”

Theirs was far from the only battle that broke out in the sixth GOP debate of the 2016 campaign season. Sen. Marco Rubio (Fla.) had intensely personal clashes with both Cruz and New Jersey Gov. Chris Christie. Rubio and Christie are both hoping to emerge from the crowded Republican field as the establishment’s champion against the forces of insurgency that Trump and Cruz represent.

Until recently, it was in both Trump’s and Cruz’s interest to avoid a direct confrontation. Cruz was leery of alienating Trump’s supporters — who might come to him, if the incendiary billionaire were to self-destruct. Trump, for his part, did not consider Cruz much of a threat.

On Thursday, they went so far as to question each other’s fitness to govern.

Trump contended that Cruz’s birth to a U.S. citizen in Canada might disqualify him from becoming president because the Constitution decrees that only a “natural born citizen” may hold the office.

“There’s a big question mark on your head. And you can’t do that to the party. You really can’t,” Trump told Cruz.

The senator from Texas retorted that Trump was motivated more by his political prospects than any constitutional concern.

“I recognize that Donald is dismayed that his poll numbers are falling in Iowa,” Cruz said. “But the facts and the law here are really quite clear. Under long-standing U.S. law, the child of a U.S. citizen born abroad is a natural-born citizen.”

Then it was Cruz’s turn to go on offense.

Repeating something he first said in a radio interview, Cruz charged that Trump had “New York values” — invoking that city’s reputation, particularly in red-state America, as the bastion of the liberal elite.

“I can frame it another way,” Cruz said. “Not a lot of conservatives come out of Manhattan. I’m just saying.”

Trump responded with indignation, saying New York City is home to “loving people, wonderful people.” He recalled the fall of the World Trade Center towers on Sept. 11, 2001, noting the “smell of death” that pervaded the city for months.

“I saw something that no place on Earth could have handled more beautifully, more humanely than New York,” Trump said. He added, “That was a very insulting statement that Ted made.”

As Trump and Cruz argued over the latter’s constitutional qualifications to be president, the other candidates struggled to get a word in. Rubio drew applause when he interjected, “I hate to interrupt this episode of Court TV, but I think we have to get back to what this election ought to be about.”

However, when Rubio and Cruz got their chance to go at it, theirs turned out to be an esoteric back-and-forth over the consistency of their Senate votes, particularly on immigration.

After Rubio ticked through votes that he described as flip-flops and political opportunism on Cruz’s part, the Texan said: “He had no fewer than 11 attacks there. I appreciate you dumping your oppo research folder on the debate stage.”

Rubio insisted: “No, it’s your record.”

At that point, former Florida governor Jeb Bush interjected: “This latest back-and-forth between two backbench senators, it explains why we have the mess in Washington, D.C.”

Christie, who has often dismissed the Senate as nothing more than a debating society, interrupted another argument between Cruz and Rubio over taxes, saying: “You’ve already had your chance, Marco. You blew it.”

The disputes that broke out during the debate, which was sponsored by Fox Business Network and included the GOP’s seven leading presidential hopefuls, have been simmering on the campaign trail in recent days. The event gave the candidates a chance to confront one another face to face, rather than through their stump speeches, surrogates and allied super PACs.

Among the Republicans, several battles are going on at once. Where Trump and Cruz are each looking to win the caucuses by claiming to be the one who can slay the old order, the field also includes a host of current and former governors and senators.

Nearly as important as which candidate comes in first place is the question of which will emerge from what is being called the “establishment lane.”

Rubio repeated his charge that Christie, the governor of a heavily Democratic state, has a record too liberal for a conservative party. He noted that Christie once supported Common Core educational standards, backed some gun-control legislation and supported Obama’s nomination of Supreme Court Justice Sonia Sotomayor.

“Our next president has to be someone that undoes the damage Barack Obama has done to this country,” Rubio said. “It cannot be someone that agrees with his agenda. . . . Unfortunately, Governor Christie has endorsed many of the ideas that Barack Obama supports.”

Turning to face Rubio, Christie accused the senator of being loose with his facts and manufacturing indignation because Christie has emerged as a political threat. He reminded Rubio that he had once called him “a conservative reformer that New Jersey needed,” but that “he’s changed his tune.”

Christie recalled October’s debate, when Rubio responded to an attack from Bush by saying someone had convinced him that Bush had to hit his onetime protege. “It appears that the same someone who has been whispering in old Marco’s ear, too,” Christie said.

As the leading candidates feuded, Ben Carson — the mild-mannered retired neurosurgeon who briefly topped the polls — urged civility. “We have to stop this because, you know, if we manage to damage ourselves and we lose the next election and a progressive gets in there and they get two or three Supreme Court picks, this nation is over as we know it,” he said.

The call did not stop Bush from going after Trump, describing his rival as “unhinged” for his policies on immigration and Muslims and misguided in his plans for high tariffs on Chinese imports.

“This would be devastating for our economy. We need somebody with a steady hand being president of the United States,” Bush said.

Trump responded with an attack on Bush’s personality.

“We don’t need a weak person being president of the United States,” Trump said, returning to an old insult that Bush is ­“low-energy.” “We don’t need that. We don’t need that.”

Trump brushed off criticism of his demeanor, saying, “I will gladly accept the mantle of anger.”

“Our military is a disaster,” he said. “Our health care is a horror show. Obamacare, we’re going to repeal it and replace it. We have no borders. Our vets are being treated horribly. Illegal immigration is beyond belief. Our country is being run by incompetent people. And yes, I am angry.”

The debate came just 48 hours after President Obama delivered the final State of the Union address of his presidency, which included sharp condemnation of the angry GOP rhetoric over Muslims, immigration and other issues. At the debate, the candidates flung zinger after zinger in an attempt to outdo one another in delivering the most visceral condemnation of both Obama and Clinton, his first-term secretary of state and the leading Democratic presidential candidate.

Christie called Obama “a petulant child” and likened his State of the Union to “storytime” because it painted, in Christie’s view, too rosy a picture of the country.

“We are going to kick your rear end out of the White House come this fall,” Christie said of Obama.

The language was just as strident in discussing Clinton. Bush suggested that she “might be going back and forth between the White House and the courthouse” because she is under FBI investigation for her email practices. Then Rubio stepped up the rhetoric and charged that Clinton was “disqualified from being commander in chief.”

When co-moderator Maria Bartiromo asked Cruz about a New York Times report Wednesday that he failed to properly disclose loans from Goldman Sachs and CitiBank during his 2012 Senate campaign, Cruz used the moment to slam “the mainstream media.”

“Yes, I made a paperwork error disclosing it on one piece of paper instead of the other,” Cruz said. “But if that’s the best the New York Times has got, they better go back to the well.”

Although Ohio Gov. John Kasich did not figure in the more contentious exchanges, he sought to appeal directly to frustrated middle- and working-class families.

“People are upset,” he said. “You’re 50 or 51 years old and some kid walks in and tells you you’re out of work and you don’t know where to go and where to turn. Do we have an answer for that? We do.”

David A. Fahrenthold in Washington contributed to this report.