Tensions between Republican presidential hopefuls Ted Cruz and Marco Rubio erupted over immigration and more Thursday night during the Fox News/Google debate, as the campaigns tried to put aside their battles with front-runner Donald Trump -- "the elephant not in the room” who chose to boycott -- and focus on the issues, and their Democratic rivals.

While the Iowa debate assumed a somewhat more subdued tone without Trump, Cruz and Rubio got into a barbed dispute over “amnesty” in the second half of the debate.

Rubio accused Cruz of falsely describing himself as the most conservative candidate, and changing his position on immigration.

“This is the lie that Ted’s campaign is built on,” the Florida senator said. “Throughout this campaign, you’ve been willing to say and do anything in order to get votes.”

He said Cruz used to talk about bringing immigrants out of the shadows, and, “now, you want to trump Trump on immigration.”

The Texas senator flipped the allegation, saying it is Rubio who vowed to fight against “amnesty” and then reversed course for political expediency.

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“I like Marco, he’s very charming, he’s very smooth,” Cruz said, before accusing him of siding with donors in the immigration debate.

The exchanges came at the final Republican debate before the Iowa caucuses on Monday.

For the first time, Trump was not on the debate stage, instead hosting a veterans event nearby in Des Moines. He boycotted the Iowa showdown over complaints about Fox News and co-moderator Megyn Kelly.

His absence gave other candidates more time, though, to engage the issues and each other. 

New Jersey Gov. Chris Christie interjected during the Rubio-Cruz spat to tout his status as a Washington outsider. 

"This is why you need to send someone outside of Washington to Washington," he said. "Stop the Washington bull and let's get things done." 

Cruz and Rubio also tangled over who would be tougher on the Islamic State, and the rancor even spilled out into tensions between the candidates and the moderators.

At one point, Cruz complained about the moderators urging the candidates to attack each other, and half-jokingly threatened to “leave the stage” if they asked another “mean question.”

Rubio mocked those comments, telling the moderators: “First of all, I’m not leaving the stage no matter what you ask me.”

Rubio also questioned Cruz’ record on supporting the military, moments after Cruz said he’d “utterly and completely destroy ISIS.”

“The only budget that Ted has ever voted for was a budget that Rand Paul sponsored that brags about cutting defense spending,” Rubio said.

Cruz, though, doubled down on comments that he’d “carpet bomb” the enemy, saying that's what was done in the first Iraq war.  

Meanwhile, the candidates dispatched with their Trump comments at the very beginning of the debate.

After Cruz was asked to “address the elephant not in the room,” he quipped: “I’m a maniac, and everyone on this stage is stupid, fat and ugly … now that we’ve gotten the Donald Trump portion out of the way.”

Jeb Bush, who used to take the brunt of Trump's debate attacks, also joked about Trump’s absence. “I kind of miss Donald Trump. He was a little teddy bear to me. We’ve always had such a loving relationship … during these debates and in between.” 

Bush later sparred as well with Rubio on immigration. Bush said Rubio sponsored the “gang of eight” bill that allowed for legalization, but “then he cut and run” because it wasn’t popular with conservatives. 

The debate marked a particular opportunity for Kentucky Sen. Rand Paul – who did not qualify for the recent Fox Business Network debate but returned to the prime-time stage Thursday after making the cut this time. 

"It's great to be back," Paul said Thursday. 

Paul, despite struggling with low poll numbers, seemed to have plenty of supporters in the audience, as his responses drew applause from the crowd several times. He also took shots at both Cruz and Rubio on their records. 

Echoing Cruz' criticism, he said Rubio made a deal with Democrats on immigration and suggested he was weak on border security. 

At the same time, Paul suggested Cruz was being disingenuous by claiming he was never for "amnesty." He said Cruz has an "authenticity problem." 

Also on stage Thursday night were retired neurosurgeon Ben Carson and Ohio Gov. John Kasich.  

Carson’s standout moment seemed to come at the end of the debate, when he used his closing statement to recite the Preamble to the U.S. Constitution.

“Please think of our founding fathers as you listen,” Carson asked. After reading aloud the Preamble -- including its call for a “more perfect union” – he said, “Folks, it’s not too late. Enough said.” 

Kasich pitched himself as a problem-solver, once again pointing to his record as Ohio’s governor.

“At the end of the day, I’m an optimist, because I’ve seen so many things get accomplished in my lifetime, and we can do it again together,” he said.  

Four candidates also participated in the earlier, 7 p.m. ET debate: Former HP CEO Carly Fiorina; former Arkansas Gov. Mike Huckabee; former Pennsylvania Sen. Rick Santorum; and former Virginia Gov. Jim Gilmore. 

Santorum and Huckabee, following the evening debate, attended the veterans event that Trump hosted nearby. 

After Trump’s rally, Fox News released a statement saying Fox News Chairman Roger Ailes had three brief conversations with the Republican candidate Thursday about possibly appearing at the debate.

“Trump offered to appear at the debate upon the condition that FOX News contribute $5 million to his charities,” a Fox News spokesperson said. “We explained that was not possible and we could not engage in a quid pro quo, nor could any money change hands for any reason. In the last 48 hours, we've kept two issues at the forefront — we would never compromise our journalistic standards and we would always stand by our journalist, Megyn Kelly. We have accomplished those two goals and we are pleased with the outcome.” 

The polls in the Hawkeye State show essentially a two-man race for first between Trump and Cruz in the final stretch. Rubio has been holding steady in third position, while Carson’s numbers have been on a downward course in recent weeks.

After Iowa, the candidates head to New Hampshire, where Trump also leads but several other candidates are jockeying for position behind him.

The debate Thursday was moderated by Fox News anchors Bret Baier, Megyn Kelly and Chris Wallace.