Newt Gingrich set his sights Sunday on Florida after a stunning win in South Carolina's presidential primary, while main Republican rival Mitt Romney bowed to pressure to release his tax returns.

Gingrich's resounding victory Saturday turned the topsy-turvy race on its head, and his political resurrection ensures a dramatic 2012 battle to be the Republican standard-bearer against President Barack Obama on November 6.

It shattered the aura of invincibility cloaking the former Massachusetts governor and turned Florida's January 31 primary into a pivotal contest that could either confirm Gingrich's momentum or restore Romney as the frontrunner.

Palm Beach County Republican Party chairman Sid Dinerstein said Florida was now the "make-or-break state" in the contest. "There is a very good chance therefore that after Florida the race is practically over," he told AFP.

"It was not a great week for me," a stung Romney conceded to Fox News Sunday after watching his substantial lead in South Carolina evaporate in a matter of days -- Gingrich eventually won by a 12.5 percentage point margin.

The campaign rhetoric grew increasingly bitter as the multimillionaire investor Romney and the pugnacious former House speaker locked horns.

There was "no question" he would go after his rival's character more strongly than he has, Romney said, implying he would call out Gingrich on his past ethics charges and his admitted marital affairs.

"Character is a big part of leadership, as is vision, sobriety, steadiness. These are attributes which I think people want to see in their candidate."

Gingrich, who appeared on three separate Sunday morning talk shows in the wake of his victory, focused his attention on savaging Obama, who he portrayed as a dangerously weak radical that had failed America in his first term.

"Beating Barack Obama has to be the number one mission of the Republican Party. A second term for Barack Obama will be a disaster for this country," Gingrich told NBC's "Meet the Press."

"I think it's important that we have a candidate strong enough and tough enough to be able to take on President Obama."

He posed himself as the insurgent street-fighter up against the establishment candidate Romney, and suggested it was best to air their differences and weaknesses now, rather than in the run up to November when Obama will use his "billion-dollar campaign" to cripple his opponent.

Gingrich's win rekindled doubts about whether the relatively moderate Romney can rally the party's conservative core, which views him with suspicion.

Gingrich was propelled into contention by some stellar debate performances, in particular a vicious counter-attack on the media when probed about an allegation by his ex-wife that he had once requested an open marriage.

But Florida is a far larger and more diverse state than South Carolina, and Romney's vaunted campaign riches and well-oiled machine weapons were expected to give him the edge here.

After coming under intense pressure from Gingrich and others, Romney vowed to release his 2010 tax return on Tuesday, seeking to dispel doubts over what he might be hiding ahead of the all-important Florida vote.

But he insisted he would not shy away from his business record, saying he believed Americans -- with respect for Congress at an all time low -- would respect private-sector success over Gingrich's record as a Washington lifer.

"Look, I don't think that the people of this country are going to choose as the next president of the United States a person who spent 40 years in Washington as a congressman and a lobbyist," Romney told Fox News Sunday.

South Carolina marked Gingrich's first triumph after Christian conservative former senator Rick Santorum squeaked out a victory in Iowa and Romney romped home in New Hampshire, dividing up the electoral spoils and bragging rights.

Santorum and libertarian congressman Ron Paul finished a distant third and fourth respectively in South Carolina, but both vowed to stay in the race.

The four remaining candidates have a first chance to impress Florida voters when they duel it out in an eagerly-awaited televised debate on Monday night in Tampa.