MIAMI -- Case closed.

Mitt Romney's lopsided Florida victory over Newt Gingrich on Tuesday -- The Associated Press projected him the winner just after 8 p.m. -- proved that the Republican front-runner can win conservatives, triumph in debates and fight a bruising campaign that can lay an opponent to waste.

Romney's Florida win also showed Republicans that he can run the kind of national campaign that can defeat President Barack

Obama in November.

"Doing well in Florida," Romney said Tuesday, "is a pretty good indication of your prospects nationally."

That's because Florida is more like the nation than any of the other three early states: Iowa, New Hampshire and South Carolina.

North Florida is the Deep South. Southwest Florida is like the Midwest. Latin America meets New York in Southeast Florida. And it all mixes together along the I-4 corridor from Tampa Bay through Central Florida.

Romney excelled in South Florida and among Hispanics, exit polls showed. Early results indicated that he might lose North Florida, but he was winning everywhere else by big margins.

"Florida is the nation's reflecting pool," said Alex Castellanos, a Republican consultant who worked for Romney in 2008 and George W. Bush in 2004.

Before the first ballot was even cast Tuesday, Romney had a cushion of early votes that could have exceeded 60,000.

While the other campaigns were silent in early January, Romney advertised on radio and television and aggressively called and mailed early voters, who cast more than 632,000 ballots.

With the big results in from Florida, Castellanos said, the Republican race is almost history, though Gingrich has vowed to fight all the way to the national convention in Tampa this summer.

"This race won't end tonight, but it will be over," Castellanos said. "Romney will have done something no other nonincumbent Republican candidate has ever done: He really only lost one of the first four contests. That's remarkable."

Technically, Romney lost Iowa, which initially declared him the winner -- only to hand it to Rick Santorum, even though ballots disappeared.

But Santorum has little chance if Florida's vote is any indication. Same with Ron Paul, who didn't campaign in Florida so he could go to smaller states with caucuses. All the candidates lack Romney's money and organization.

Nevada will hold its caucus Saturday, and Romney is expected to win in that state, which has a heavy population of fellow Mormons. Gingrich already is lowering expectations there.

There also are no debates until Feb. 22. Until Florida, Gingrich was viewed as the great debater, but Romney edged him in Florida's two debates -- and two-thirds of voters said the debates made a difference, exit polls showed.

The exit polls suggested that Romney, who highlighted foreclosures as a problem, might have won on the issues.

Only 20 percent felt they were getting ahead financially, half described foreclosures as a major community problem and about 60 percent felt the economy mattered most in choosing a candidate.

If Romney can keep communicating that message, he's sure to do well in Arizona and Michigan, which share Florida's hard financial times.

Another potential edge for Romney is that his father was governor of Michigan, and Arizona is home to a large Mormon population and temple. Also, polls suggest that Arizona Republicans favor Romney's hard-line immigration stances more than Gingrich's.

Still, Gingrich is expected to do well in Southern primaries from his home state of Georgia to Tennessee.