(CNN) -- Mitt Romney attacked surging conservative Newt Gingrich in a Florida debate and prepared to face questions Tuesday about his tax returns being released under pressure in a crucial week for the Republican presidential race.
In the spirited Monday night debate at the University of South Florida in Tampa, Romney questioned the former House speaker over his record in Congress and alleged lobbying after getting out of government.
Gingrich, who also came under criticism from rivals Rick Santorum and Ron Paul, tried to remain calm and exude a presidential demeanor as polls show his campaign strengthening after his victory in last week's South Carolina primary.
However, Gingrich angrily denied the lobbying accusation by Romney, accusing him of lying about the issue and seemingly flustered by the persistent attack.
Pausing at one point to collect his thoughts, Gingrich said Romney had been "walking around this state saying things that aren't true."
Romney continued, though, later saying to Gingrich: "You could call it whatever you like; I call it influence peddling."
The exchange was the sharpest of the debate, the first of two in Florida this week ahead of the January 31 primary in the Sunshine State.
Responding to the opening questions in the debate sponsored by NBC News, the National Journal and the Tampa Bay Times, in collaboration with the Florida Council of 100, Romney repeated attacks on Gingrich that he has stepped up since Gingrich's victory Saturday in South Carolina and rise in recent polls.
"Members of his own congressional team after four years of his leadership, they voted to replace him," Romney said of Gingrich's time as House speaker from 1995 to 1999.
Romney also said contracts from Gingrich's work for federal mortgage giant Freddie Mac showed that Gingrich was hired by the chief lobbyist for the group.
"You were hired by the chief lobbyist of Freddie Mac, not the CEO, not the head of public Affairs -- by the chief lobbyist at Freddie Mac," Romney said. "You also spoke publicly in favor of these GSEs, these government-sponsored entities, at a very time when Freddie Mac was getting America in a position where we would have had a massive housing collapse. You could have spoken out aggressively. You could have spoken out in a way to say these guys are wrong, this needs to end. But instead, you were being paid by them."
Gingrich shot back that "I have never, ever gone and done any lobbying."
"In fact, we brought in an expert on lobbying law and trained all of our staff," he said. "And that expert is prepared to testify that he was brought in to say here is the bright line between what you can do as a citizen and what you do as a lobbyist. And we consistently, for 12 years, running four small businesses, stayed away from lobbying, precisely because I thought this kind of defamatory and factually false charge would be made."
Gingrich also denied paying a fine for a congressional ethics violation while he was speaker, saying it was reimbursement for "the cost of going through the process" of determining one problem in his case.
He depicted his departure from Congress as taking responsibility for a poor Republican election result in 1998, but Paul -- a House member from Texas since 1997 -- disputed him.
"He didn't have the votes" to continue as speaker, Paul said. "That was what the problem was. So this idea that he voluntarily reneged and he was going to punish himself because we didn't do well in the election, that's just not the way it was."
Gingrich has cut the lead held by Romney in Florida and also caught the former Massachusetts governor in a national poll released Monday. One reason for the changing dynamic is Romney's uncertain response to calls for him to release his tax returns.
He first said he would do so in April, but under increasing pressure from opponents and some supporters, Romney agreed to do so on Tuesday.
Asked about what people should expect, Romney said he expected to face questions about details of his wealth but added: "I pay all the taxes that are legally required and not a dollar more."
"I don't think you want someone as the candidate for president who pays more taxes than he owes," Romney said.
Santorum, who is vying with Gingrich for conservative support, repeated his attack from the campaign trail that Gingrich and Romney are vulnerable on key issues for the political right, including health care reform.
According to Santorum, Romney's health care law in Massachusetts was the model for the federal act pushed by President Barack Obama and passed by Democrats, while Gingrich supported a federal mandate for health insurance for years before changing his stance on an issue deplored by conservatives.
Santorum, a former Pennsylvania senator, also said both candidates have supported capping carbon emissions as part of a legislative response to climate change, which he said went against conservative principles.
Arguing against Republicans who have "rejected conservatism when it became hard to stand" against public pressure, Santorum said that in future battles faced by the next president, "it's going to be easy to bail out and compromise your principles."
When the topic turned to foreign policy, Gingrich and Romney took hardline stances, advocating a military response against any Iranian effort to block the Strait of Hormuz. Gingrich also supported everything short of a military invasion to overthrow the Cuban government, trying to appeal to a strong Cuban-American community in Florida.
"I'm talking about using every asset available to the United States, including appropriate covert operations ...," Gingrich said, later adding: "... we have to minimize the survival of the dictatorship and to maximize the chance for freedom in Cuba."
Paul, meanwhile, persisted in his policies to reduce U.S. military presence around the world, saying in response to Gingrich's Cuba remarks that "the Cold War is over."
Calling instead for opening relations with Cuba, he said: "It's not 1962 anymore."
"We don't have to use force and intimidation," Paul said to some applause from the debate audience.
On another issue of interest to Florida voters, Gingrich and Romney called for bolstering the U.S. space program by soliciting commercial investment.
Gingrich said setting specific goals such as a permanent presence on the moon and then establishing prizes for meeting them would spur an "amazing" private sector response, while Romney advocated a collaborative approach involving commercial, government, military and educational support.
With the first three contests of the nominating process producing three different winners -- Santorum in Iowa, Romney in New Hampshire and Gingrich in South Carolina -- Florida is a key battleground and offers a different campaign landscape.
The number of Florida Republican voters exceeds the combined total in the previous three states, requiring a larger campaign organization and more money to buy advertising. Romney got a head start in the state over his rivals and also is expected to receive a boost from early voting permitted in Florida.
According to the state, at least 53,000 ballots have been cast in early voting that started statewide on Saturday, and 475,000 people requested and were sent absentee ballots, with 180,000 filled out and sent back by last Wednesday.
Those absentee votes came in before Gingrich skyrocketed in the polls and won South Carolina's primary by a double-digit margin.
Overall, nearly 1.95 million people voted in the 2008 Florida GOP primary.
According to the latest results from Gallup's daily tracking poll, Gingrich is in a statistical tie with Romney nationally among registered Republicans.
The national poll showed Romney at 29% and Gingrich at 28%. After the New Hampshire primary earlier this month, Romney was at 37% support and Gingrich at 14% in the same poll.
Monday's poll results showed Paul at 13% and Santorum at 11%. The sampling error was plus-or-minus three percentage points.
Paul took part in Monday's debate but otherwise is not spending much money or time in Florida.
With little chance of winning, Paul chose not to compete in state where first place gets all the delegates. Instead, Paul is focusing on upcoming caucuses in Nevada, Colorado and Minnesota.
The GOP nomination fight has changed dramatically over the course of the past week.
Initially announced as the victor in the January 3 Iowa caucuses by eight votes over Santorum, Romney learned Thursday that certified results showed Santorum actually won the state by 34 votes.
Then came Gingrich's solid victory Saturday in South Carolina, in a race that Romney had led until his uncertain handling of whether to release his tax returns and a pair of debates widely considered to have been won dominated by the former speaker.
CNN's Paul Steinhauser and Ashley Killough contributed to this report.