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“If people don’t get work here, they’re going to self-deport to a place where they can get work,” he said.

Fighting to stay relevant in the race, Mr. Santorum, the belated winner of the Iowa caucuses, warned that Mr. Romney and Mr. Gingrich sold out basic conservative principles by supporting the $700 billion Wall Street bailout, “cap-and-trade” related proposals and an individual health insurance mandate, which Mr. Romney supported on the state level and Mr. Gingrich supported on the federal level for “20 years.”

“When push came to shove, they got shoved, they didn’t stand tall for conservative principles,” Mr. Santorum said. “They rejected conservatism when it was hard to stand.”

When the debate turned to the issue of Cuba, Mr. Romney said President Obama was wrong to ease the travel restrictions, while Mr. Gingrich said the policy of his presidency would be to overthrow the regime of Fidel Castro.

“A Gingrich presidency,” the Georgia Republican vowed, “will not tolerate four more years of this dictatorship.”

Mr. Paul said he would move in the opposite direction. “I think we’re living in the Dark Ages when we can’t even talk to the Cuban people,” he said. “I think it’s not 1962 any more, and we don’t have to use force and intimidation and overthrow of governments.”

Mr. Romney also assured moderator Brian Williams that there will be “no surprises” when he releases his tax records from 2010 and 2011 — a decision that he made after coming under significant pressure from his competitors, particularly Mr. Gingrich.

“You’ll see my income, how much taxes I paid, how much I paid to charity,” he said. “You’ll see how complicated taxes can be. But I pay all the taxes that are legally required and not a dollar more.”

The back-and-forth between Mr. Romney and Mr. Gingrich dominated the first hour of the two-hour debate here at the University of South Florida, while Mr. Santorum and Mr. Paul watched on in silence.

The two men telegraphed their attacks earlier in the day, with Mr. Romney launching a blistering multi-pronged attack against Mr. Gingrich’s work as a “lobbyist,” calling on him to release his contract and even suggesting that he could be guilty of some potential wrongdoing for the work he did on behalf of Freddie Mac.

Mr. Romney kicked off Monday morning by calling on Mr. Gingrich to release the records from the ethic investigations that played a part in his ouster as House speaker in 1999, as well as a list of the clients that he worked for when he lobbied lawmakers for Medicare Part D.

“Was he working or were his entities working with any health care companies that could have benefited from that? That could represent not just evidence of lobbying, but potentially wrongful activity of some kind,” Mr. Romney said, before calling on Mr. Gingrich to also release the consulting contacts he received from Freddie Mac.

Along the way, Mr. Romney mocked Mr. Gingrich’s argument that he advised Freddie Mac as a “historian,” saying, “If it walks like a duck and quacks like a duck, it’s a duck.”

The Romney camp also rolled out a new “Florida Families” television ad that paints Mr. Gingrich’s ties in Freddie Mac in a negative light.

“While Florida families lost everything in the housing crisis, Newt Gingrich cashed in,” the narrator says. “Gingrich was paid over $1.6 million by the scandal-ridden agency that helped create the crisis.”

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