Ted Cruz and Donald Trump clashed in a spectacular way at the Republican presidential debate Thursday, engaging in a rapid-fire and quick-witted exchange over Cruz’ eligibility for office – and later, a dispute in which Trump cited 9/11 to put down his rival’s jokes about “New York values.”

The tension between the two men, who until now have maintained a certain peace on the debate stage, was palpable. Trump essentially admitted he’s now getting tougher on Cruz because he’s rising in the polls in Iowa – and gave no ground over the course of more than two hours.

While all seven candidates on the prime-time Fox Business Network debate stage spent much of their time attacking President Obama and Hillary Clinton, the Trump-Cruz battle on display could set the tone for the final run-up to Iowa and New Hampshire.

In perhaps his most withering retort, Trump slammed Cruz for questioning “New York values.” Recalling memories from after 9/11, Trump described the “horrific” clean up and the “smell of death” in the city.

“It was with us for months, the smell,” Trump said. “And everybody in the world loved New York, loved New Yorkers -- and I have to tell you, that was a very insulting statement.”

On the question of Cruz’ eligibility, however, the Texas senator arrived well-prepared to rebut the GOP front-runner’s claims that his Canadian birth might make him unable to run for office.

He noted Trump ignored the questions last year, and alleged he was only going after the issue because of the polls.

“The Constitution hasn’t changed, but the poll numbers changed,” Cruz said.

Then, in a retort reminiscent of Reagan’s famous “youth and inexperience” quip, Cruz tried to flip the script by noting some “birther theories” also say a candidate must have two parents born on U.S. soil to be eligible to run.

Pointing out Trump’s mother was born in Scotland, Cruz said: “On the issue of citizenship, I’m not going to use your mother’s birth against you.”

Trump said, “But I was born here … big difference.”

This touched off a heated exchange, punctuated by frequent, thunderous boos and applause from the audience.

Trump argued that Cruz is exaggerating his poll numbers – “he’s doing better, he’s got probably a 4 or 5 percent chance,” he said -- but maintained that Democrats could use the questions to file suit against him.

And if he won, Trump said, “Who the hell knows if you can even serve in office?”

He called the issue a “big overhang” and said, “You can’t do that to the party.”

Trump also toyed with the idea of naming Cruz his running mate, and Cruz extended the same offer – but Trump said he’d probably “go back to building buildings” if he lost.

Florida Sen. Marco Rubio then interjected to talk about other issues.

“I hate to interrupt this episode of court TV,” Rubio said.

The moment of levity was fleeting, with the two later tangling over Cruz’ “New York values” comments. Before Trump offered his somber memory of 9/11, Cruz said, “Not a lot of conservatives come out of Manhattan. I’m just saying.”.

The exchanges, at times, seemed to relegate the other five candidates to a debate among themselves, though most on stage put on an energetic performance.

Rubio and New Jersey Gov. Chris Christie -- who are battling with Cruz, Ohio Gov. John Kasich and former Florida Gov. Jeb Bush for the No. 2 position in New Hampshire – tangled at one point over Christie’s conservative credentials. Christie fired back by suggesting Rubio was just playing politics.

At another point, the New Jersey governor cut off Rubio when he tried to elaborate on entitlements, saying, “You had your chance” and “blew it.”

Cruz and Rubio also tangled over immigration, with Rubio claiming Cruz has reversed course on several fronts. “That is not consistent conservatism, that is political calculation,” he said.

“I appreciate you dumping your oppo research folder on the debate stage,” Cruz countered, maintaining that he opposes “amnesty” while Rubio backs citizenship for illegal immigrants.

Bush chimed in to mock the debate between the “back-bench senators.”

Meanwhile, Cruz took aim at one of his favorite targets, the media – criticizing The New York Times for a critical report about a campaign finance disclosure mistake. He said if that’s the best the Times has, “they better go back to the well.”

Despite the intra-party battles, the candidates tried to focus their attention on Obama and Clinton.

Bush ripped the Democratic front-runner for being at the heart of an FBI probe over her email set-up, saying if elected, “she might be going back and forth between the White House and the courthouse.”

Rubio added that Clinton would actually be “disqualified.”

At the opening of the debate, the candidates slammed the president’s “rosy” State of the Union address earlier in the week.

“I watched story-time with Barack Obama, and I gotta tell you, it sounded like everything in the world was going amazing,” Christie said.

Cruz also ripped Obama for omitting any mention of the U.S. sailors detained by Iran in his State of the Union. “It was heartbreaking,” he said. Those sailors were later released.

Cruz also slammed Obama for saying in the same address that anyone knocking the economy is “peddling fiction.”

“The president tried to paint a rosy picture of jobs,” Cruz said.

The debate Thursday was among the last before the kick-off nominating contests of 2016.

The only other debate before the Iowa and New Hampshire contests will be held Jan. 28. The tight calendar has fueled the new tensions in the GOP race, particularly as Cruz challenges Trump for the lead in Iowa.

The Republican front-runner also has been engaged in an unusual battle on the sidelines with South Carolina Gov. Nikki Haley, who was tapped to give the official GOP response to President Obama’s State of the Union address Tuesday. Haley urged Americans to ignore the “angriest voices,” and later acknowledged she was referring to Trump and others.

Trump, asked about the remarks at the debate, seemed to brush off the challenge.

“I’m very angry… and I will gladly accept the mantle of anger,” he said.

Trump also stood by his controversial call to temporarily bar Muslims from entering the country – to which Bush repeated his charge that the plan is “unhinged.”

Kasich, as before, cast himself as a practical problem-solver with fiscal conservative credentials. Retired neurosurgeon Ben Carson was also asked about whether Bill Clinton’s past indiscretions are a fair topic.

“Here’s the real issue, is this America anymore? Do we still have standards? Do we still have values and principles?” he said, pointing to divisiveness in the country. “We need to start once again recognizing that there is such a thing as right and wrong. And let's not let the secular progressives drive that out of us.”

An earlier evening debate featured three lower-polling candidates -- former HP CEO Carly Fiorina; former Arkansas Gov. Mike Huckabee; and former Pennsylvania Sen. Rick Santorum. Kentucky Sen. Rand Paul qualified but did not attend. Hours later at the prime-time debate, a very brief protest broke out when some started chanting, “We want Rand.”

The debates were held at the North Charleston Coliseum and Performing Arts Center in North Charleston, S.C.