Jacksonville, Florida (CNN) -- Front-runners Mitt Romney and Newt Gingrich got the most attention and Romney appeared to get the better of his opponent on a couple of occasions during the final debate before Tuesday's critical Florida primary.

While his attacks Thursday night on his rival weren't sharp, Romney was forceful and had Gingrich on his heels when he brushed accusations aside and turned them back on Gingrich at the CNN/Republican Party of Florida debate in Jacksonville.

"Romney won two ways tonight," said CNN contributor and Republican strategist Alex Castellanos. "One, by having a good debate and two by having [Rick] Santorum have his best debate yet."

Romney appeals to the more moderate wing of the Republican Party while Santorum and Gingrich are competing for the conservative vote.

Asked to address the housing crisis, one of the major problems facing Florida voters, Gingrich began by claiming that Romney was knowingly and "unfairly" attacking him on his consulting record for mortgage giant Freddie Mac, sparking a fiery back-and-forth over which candidate has had a closer relationship with troubled lenders.

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Gingrich claimed that Romney had profited off of investments in both Fannie Mae and Freddie Mac. In turn, Romney tried to explain the nature of his investments, quickly pointing out that he may own bonds, but anything he owns is controlled by a "blind trust."

Then he asked, "Have you checked your own investments, Mr. Speaker?" and pointed out that Gingrich also has investments in the mortgage lenders, a remark that got a response from the crowd.

Thursday's audience did play a bigger part in the debate, in contrast to the other Florida debate on Monday, at which attendees were asked to hold their applause.

Also in contrast was Romney's approach, standing casually with a hand in his pocket for most of the two hours, directing his answers to the audience instead of at Gingrich as he had in Monday's debate.

Florida is the next state to vote in the already volatile nominating season with Santorum, Romney and Gingrich winning the first three contests in Iowa, New Hampshire and South Carolina, respectively.

Romney drew frequent applause early in the debate when he pushed back attacks by Gingrich over immigration.

Gingrich charged Romney's immigration policy would result in the deportation of grandmothers who are in the country illegally. Romney has advocated for "self-deportation," a policy that involves making economic conditions so difficult for undocumented workers that they choose to leave the country to find better opportunities.

The former House speaker said Romney was the most anti-immigrant candidate on the debate stage, which prompted outrage from Romney.

"I'm not going to go find grandmothers and take them out of them homes and deport them," Romney said, accusing Gingrich of using "highly-charged epithets" irresponsibly. "Our problem is not 11 million grandmothers."

However, Gingrich and Santorum, a former Pennsylvania senator, did agree with Romney that at least some illegal immigrants would be likely to "self-deport" if the government were to crack down on employers who hired illegal immigrants. All three men advocated a system of identification for immigrants that would help employers verify an employee's legal status.

Trying to widen what was becoming a two-man debate, moderator Wolf Blitzer asked Santorum and Texas Rep. Ron Paul, the candidates flanking Gingrich and Romney, if they believed any profits earned from investing in the government-backed entities should be returned.

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"That subject doesn't really interest me," Paul replied.

For his turn, Santorum launched into a screed against the personal turn the campaign has taken of late, asking that the debate shift back to the issues facing the country rather than the financial dealings of two candidates.

"The bigger issue here is, these two gentlemen, who are out distracting from the most important issues -- we have been playing petty personal politics, can we set aside that Newt was a member of Congress and used the skills that he developed as a member of Congress to go out and advise companies -- and that's not the worst thing in the world -- and that Mitt Romney is a wealthy guy because worked hard and he's going out and working hard? And you guys should leave that alone and focus on the issues."

The day before the debate, Gingrich told an audience on Florida's Space Coast, hit hard by the end of the space shuttle program, that he would build a colony on the moon by the end of his second term in office -- a plan that found little support among his rivals on stage. Santorum said the depth of the debt crisis was too severe to consider such proposals. Romney said that even as a private sector suggestion, the idea was deeply flawed.

Citing his business experience, Romney said that if an executive had come to him suggesting spending "billions" of dollars on a colony on the moon, "I'd say 'You're fired.'"

Paul continued to walk his lonely path, vowing to cut back on many of the United States' investments in the military, health care and other government services. The candidate often injected humor into the debate when he proclaimed himself uninterested in many of the topics argued over by the other candidates in favor of a strict constructionist view.

Earlier in the day, Gingrich lashed out at Romney, accusing him of engaging in sleazy negative politics and being part of a fragile establishment desperate to stop the former House speaker from winning the GOP nomination.

"Many of you have probably noticed a number of attack ads and all sorts of junk, and that's what it is," Gingrich told a crowd in Mount Dora. "This is the desperate last stand of the old order throwing the kitchen sink, hoping something sticks."

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They're trying to "drown us in enough mud, raised with money from companies and people who foreclosed on Floridians," Gingrich claimed. "Remember the Republican establishment is just as much as an establishment as the Democratic establishment, and they are just as determined to stop us. ... This is a campaign for the very nature of the Republican Party and the very opportunity for a citizen conservatism to defeat the power of money and to prove that people matter more than Wall Street."

Romney, meanwhile, said before Thursday's debate he would focus on his opponent in the general election rather than his rivals on stage.

"We're going to have some choice time talking about the president and his failures, we'll probably talk a great deal about his State of the Union address and how badly mischaracterized he has described our nation at a time when so many people are suffering in this state and across the country," he said.

But "we may talk about the differences between ourselves as well," he added. "There may be some give and take."

One of Romney's most prominent supporters, however, didn't hesitate to attack Gingrich on Thursday. Former GOP presidential nominee Bob Dole released a statement through the Romney campaign characterizing Gingrich as erratic, unreliable and certain to lead the Republican Party to defeat in November.

When Gingrich was in Congress, he "was a one-man-band who rarely took advice. It was his way or the highway," Dole, a former U.S. senator from Kansas, said. As speaker, Gingrich "had a new idea every minute and most of them were off the wall. ... Democrats are spending millions of dollars running negative ads against Romney as they are hoping that Gingrich will be the nominee."

The latest public opinion polls suggest that the battle for Florida's 50 winner-take-all delegates -- the largest catch so far this primary and caucus season -- is turning into a two-man race between Romney and Gingrich. According to a CNN/Time/ORC International survey released Wednesday, 36% of people likely to vote in Tuesday's Republican primary in Florida say they are backing Romney as the party's nominee, with 34% supporting Gingrich. Romney's 2-point margin over Gingrich is well within the survey's sampling error.

The other two candidates are far behind, with Santorum at 11% and Paul at 9%, with 7% unsure of who they'll vote for.

Gingrich received a boost in the polls after his double-digit victory in Saturday's South Carolina primary, but Wednesday's CNN poll and another by the American Research Group indicate that the former House speaker's momentum might be waning.

And Monday's debate in Tampa might not have helped Gingrich, as he repeatedly came under attack by Romney, Santorum and Paul over his record as House speaker in the 1990s, characterizations of influence-peddling after getting out of government and his past stance on health care reform. Gingrich didn't seem to mount an effective response to many of the attacks.

With five days to go until the primary, the CNN/Time/ORC poll indicates that a quarter of likely primary voters say they may change their mind on which candidate they are backing.