TAMPA, Fla. — A suddenly scrambled Republican presidential contest now shifts to Florida, a day after Newt Gingrich stopped Mitt Romney’s sprint to the GOP nomination by scoring a convincing victory in South Carolina.

The air of inevitability that surrounded Romney’s candidacy just days ago is gone, at least for now. And his rivals, led by Gingrich, have 10 days before Florida’s Jan. 31 contest to prove South Carolina was no fluke.

Florida, being much larger, more diverse, and more expensive, brings new challenges to Gingrich, who again must overcome financial and organizational disadvantages as he did Saturday.

“We don’t have the kind of money at least one of the candidates has. But we do have ideas. And we do have people,” Gingrich, the former House speaker, told cheering supporters Saturday night. “And we proved here in South Carolina that people power with the right ideas beats big money. And with your help, we’re going to prove it again in Florida.”

Romney struck a defiant tone before his own backers gathered at the South Carolina State Fairgrounds, saying: “I will compete in every single state.” And wasted no time jabbing at Gingrich, saying: “Our party can’t be led to victory by someone who also has never run a business and never led a state.”

Former Pennsylvania Sen. Rick Santorum, having finished third in South Carolina, vowed to compete in Florida and beyond. His presence in the race ensures at least some division among Florida’s tea party activists and evangelicals, a division that could ultimately help Romney help erase any questions about his candidacy by scoring a victory of his own a week from Tuesday.

Texas Rep. Ron Paul likely will not be a factor in Florida, having declared that he’s bypassing the expensive state in favor of smaller subsequent contests.

As the first Southern primary, South Carolina has been a proving ground for Republican presidential hopefuls in recent years. Since Ronald Reagan in 1980, every Republican contender who won the primary has gone on to capture the party’s nomination.

Returns from 95 percent of the state’s precincts showed Gingrich with 41 percent of the vote to 27 percent for Romney. Santorum was winning 17 percent, Paul 13 percent.

But political momentum was the real prize with the race to pick an opponent to President Barack Obama still in its early stages.

Already, Romney and a group that supports him were on the air in Florida with a significant television ad campaign, more than $7 million combined to date.

Gingrich readily conceded that he trails in money, and even before appearing for his victory speech he tweeted supporters thanking them and appealing for a flood of donations for the Jan 31 primary. “Help me deliver the knockout punch in Florida. Join our Moneybomb and donate now,” said his Internet message.

Aides to Romney, the former Massachusetts governor, had once dared hope that Florida would seal his nomination — if South Carolina didn’t first — but that strategy appeared to vanish along with the once-formidable lead he held in pre-primary polls.

Romney swept into South Carolina 11 days ago as the favorite after being pronounced the winner of the lead-off Iowa caucuses, then cruising to victory in New Hampshire’s first-in-the-nation primary.

But in the sometimes-surreal week that followed, he was stripped of his Iowa triumph — GOP officials there now say Santorum narrowly won — while former Utah Gov. Jon Huntsman dropped out and endorsed Romney and Texas Gov. Rick Perry quit and backed Gingrich.

Romney responded awkwardly to questions about releasing his income tax returns, and about his investments in the Cayman Islands. Gingrich, the former speaker of the House, benefited from two well-received debate performances while grappling with allegations by an ex-wife that he had once asked her for an open marriage so he could keep his mistress.

By primary eve, Romney was speculating openly about a lengthy battle for the nomination rather than the quick knockout that had seemed within his grasp only days earlier.