Desperate for a good debate performance to help restore momentum for his U.S. presidential campaign, Mitt Romney came out swinging in Monday's Republican debate with sharp attacks on Newt Gingrich as an influence peddler who resigned as House speaker in disgrace.

Stung by Gingrich's convincing victory in South Carolina on Saturday, Romney has been striking back with attacks on Gingrich, trying to rebuild momentum for his campaign in Florida, whose January 31 primary could play a major role in determining who will be the Republican presidential nominee.

Romney kept on message in the debate, repeatedly seeking to tar the former speaker of the U.S. House of Representatives as a Washington insider who lobbied for clients including the troubled mortgage giant Freddie Mac.

In the 15 years after he left the speakership, the speaker has been working as an influence peddler in Washington, Romney said in one of several fiery exchanges with Gingrich.

Gingrich shot back that Romney was not telling the truth. He's said at least four things that are false, he said. Briefly assuming the role of front-runner, he looked ahead to November's general election, and said the debate should focus on how to beat Democratic President Barack Obama.

Romney took a much tougher tone than he did last week during a debate in South Carolina, when he stumbled in response to questions about his tax records.

On Monday, he used a question about his tax returns as an opportunity to outline his proposals to change the tax system by cutting capital gains and corporate taxes. And he joked that the country needs to get more people back to work so they can begin to pay taxes.

TAX RETURNS

The former Massachusetts governor, one of the wealthiest U.S. presidential candidates in history, has promised to release his 2010 tax return and his estimated 2011 taxes on Tuesday, but has been criticized for failing to release many years' records.

I'm putting out two years, which is more than anyone else on this stage. I think it'll satisfy the interests of the American people to see that I pay my taxes, where I give my charitable contributions to, and I think that's the right number, Romney said.

To distract from questions about his own financial situation, Romney had called on Gingrich before the debate to disclose his contract for the government-sponsored mortgage financing giant Freddie Mac, for which Gingrich made $1.6 million (1 million pounds).

Shortly before the debate, Gingrich's former consulting firm released a contract Gingrich signed with the company in 2006, but it shed little light on what Gingrich was hired to do. The document called for a $300,000 retainer and $25,000 in fees monthly for the year.

Gingrich denies his work for the mortgage giant made him a lobbyist, but Romney insists it did, making his case that Gingrich is a creature of Washington.

The mortgage issue has particular resonance in Florida, one of the states hardest hit by the collapse of the U.S. real estate market. It has contributed to a state unemployment rate of 9.9 percent, above the national average.

Gingrich trounced Romney in South Carolina's Republican primary, after a series of strong debate performances.

New opinion polls show that Gingrich has jumped into the lead in Florida.

The remaining two candidates, Texas Representative Ron Paul and former Pennsylvania Senator Rick Santorum, are seeking to make a mark after finishing far behind in South Carolina. But neither had much of an impact in the first part of the discussion as the two leaders traded insults and barbs.

The debate, sponsored by NBC, National Journal and the Tampa Bay Times, was the 18th of the 2012 election cycle, and the first of two debates this week. A second is scheduled for Jacksonville on Thursday.

A Romney victory in Florida would blunt Gingrich's surge and restore the lustre of his campaign. Gingrich wants to deliver what he has called the knockout punch.

Gingrich has used the debates to his advantage, helping him rise from a bitter fourth-place finish in Iowa to victory in South Carolina.

(Additional reporting by Steve Holland; writing by Steve Holland and Patricia Zengerle; editing by Peter Cooney and Mohammad Zargham)