By Steve Holland and Ros Krasny

JACKSONVILLE, Florida (Reuters) - Republican presidential hopeful Mitt Romney took the fight to chief rival Newt Gingrich on Thursday in his most aggressive debate performance yet, five days ahead of Florida's primary vote.

A neck-and-neck race for Florida and its importance for the Republican presidential nomination made for a combustible atmosphere at the University of North Florida in Jacksonville as the candidates sparred repeatedly.

Gingrich, who has displayed a mastery of debating skills during previous debates, was frequently caught flat-footed under attack from Romney who went after his chief rival in an attempt to put his campaign back on track after losing South Carolina last Saturday.

Gingrich and Romney are running close in polls before next Tuesday's primary vote in Florida, the biggest state so far in the early voting for the Republican nomination to face President Barack Obama in November. The most recent polls put Romney ahead.

Romney, a former Massachusetts governor, took umbrage at Gingrich's description of him as "anti-immigrant."

"That's inexcusable," Romney said, turning to his rival. "I'm not anti-immigrant. My father was born in Mexico. ... The idea that I'm anti-immigrant is repulsive. Don't use a term like that."

Gingrich, who has offered a softer version of immigration policy than most Republican conservatives, insisted the United States could not rationally deport millions of people and that some who had lived here for decades should be allowed to stay.

But he added some confusion to his position by saying he would support some version of "self-deportation," the very issue he has criticized Romney for supporting.

"Newt needed a big night to turn around the momentum and he didn't get it. He struck me as tired and too ticked for his own good," wrote conservative columnist Rich Lowry on the National Review's website. His blog post was titled "Newt's worst night."

GINGRICH ATTACK FELL FLAT

Gingrich has enjoyed support from rock-ribbed conservatives in debate audiences by attacking debate moderators.

But this time, his effort to chastise CNN moderator Wolf Blitzer over a question about Romney's tax disclosures fell flat when Blitzer stood his ground and insisted Gingrich explain a comment he made in a TV interview that Romney "lives in a world of Swiss bank and Cayman Island bank accounts.

Gingrich did draw attention to Romney's vast wealth, which was put under the microscope this week when the former private equity executive release two years of tax documents.

"I don't know of any American president who has had a Swiss bank account. I'd be glad for you to explain that sort of thing," he said.

But Gingrich was ridiculed by Romney, Rick Santorum and Ron Paul for telling laid-off space workers near Cape Canaveral on Wednesday that if elected president next November he would seek to build a permanent colony on the lunar surface.

It was the kind of claim that supports criticism that Gingrich has grandiose yet far-fetched ideas.

Romney said the money could be better spent elsewhere, that Gingrich's proposal was a big idea but not a good one. Paul, a Texas congressman and libertarian, got off the zinger of the night.

"I don't think we should go to the moon," said Paul. "I think maybe we should send some politicians up there."

Bickering erupted from the first question over illegal immigration, and intensified over Gingrich's past work for the troubled mortgage giant Freddie Mac.

Romney raised Gingrich's work for Freddie Mac as a sign that his rival was an influence peddler, a "horn tooter" for Freddie Mac. Romney has attacked Gingrich all week for accepting $1.6 million in consulting fees from Freddie Mac.

Gingrich fought back. "Romney made $1 million dollars on Fannie Mae and Freddie Mac," he said, an attack that fell flat when Romney pointed out that Gingrich owns stock in the two government-sponsored entities at the heart of the U.S. housing crisis.

The candidates, asked which of their wives would make the best first lady of the White House, chose their own, except for Gingrich, who said they would all be terrific, including his wife, Callista.

"I would rather just talk about why I like Callista, and why I'd like her to be first lady, but she's not necessarily in any way better. These are wonderful people, and they would be wonderful first ladies," he said.

(Editing by Alistair Bell and Eric Beech)