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He offered no new policy prescriptions to help people whose homes are worth less than they owe, and suggested that the best remedy was a stronger economy. But in contrast to earlier statements he and other Republican candidates have made about letting the market correct itself by first hitting bottom, Mr. Romney, a former governor of Massachusetts, instead offered a reassuring if vague message: “People in Florida have seen home values go down,” he said, striking an empathetic tone. “It’s time to turn that around.”

Among those cheering for Mr. Romney was Eric Brandon, 41, a nurse who paid close to half a million dollars for his two-story, four-bedroom home in Palm Coast, Fla., in 2005. Now it is worth only about $130,000, he said. And he felt that Mr. Romney, as a successful businessman, was best poised to confront the problem.

“As long as people have jobs, they will be able to buy houses,” he said “The economy is my issue, and I know Romney is strong on that.”

The Republican presidential campaign is now moving into a state consumed by the housing crisis, perhaps the most enduring legacy of the economic downturn, and the primary battle is the first serious test of how it plays out as a political issue in the race. For Republicans, it is an especially tricky topic, forcing them to balance their free-market instincts against intense demand among homeowners for more to be done.

The candidates have not offered detailed plans of how to respond to the crisis, although Mr. Romney has opposed giving help to homeowners facing the loss of their homes, while Mr. Gingrich has faulted banks for being too quick to foreclose.

But seeing an opening to win over Florida voters on an issue that hits home, Mr. Romney on Monday attacked Newt Gingrich’s ties to the giant mortgage lender Freddie Mac, saying Mr. Gingrich had profited while homeowners suffered.

In interviews across Florida over the last several days, likely Republican primary voters echoed sentiments similar to Mr. Brandon’s, indicating that in a state where one in every 360 housing units is in foreclosure, and where the economy is lagging behind much of the rest of the nation, Mr. Romney’s business background could serve him well because of perceptions that he might have a better sense of how the economy works than his Republican rivals.

But his past statements about allowing market forces to address the problem continue to be a challenge for Mr. Romney. Since arriving in Florida on Sunday, Mr. Romney has been slightly moderating his tone on foreclosures, telling people in Tampa Bay on Monday that “the idea that somehow this is going to cure itself all by itself is unreal” and, “There’s going to have to be a much more concerted effort to work with the lending institutions and help them take action.”

That is a shift in emphasis from an interview in October with the editorial board of the Las Vegas Review-Journal, he said, “Don’t try and stop the foreclosure process,” adding, “let it run its course and hit the bottom.”

Mr. Gingrich has criticized banks as profiting from foreclosures, and has said he would like to repeal policies stemming from the Dodd-Frank financial overhaul, which he says are keeping small banks from making loans. He wants to change the rules to encourage banks to do more short sales of so-called underwater properties.

Some of the anger over the foreclosure crisis is directed at President Obama, who many say has not done enough to address the issue.

In parts of Florida such as Homestead and Florida City, the anger driving some of the Republican vote is visible on the street. For several hours Saturday, Carols Castellano Triana, the owner of a painting business, held a hand-painted sign saying, “Vote Republican” at the busy intersection of Palm Avenue and Dixie Highway in Florida City, an area that has been ravaged by the housing implosion.

Mr. Triana is a renter with aspirations of owning a home. He is an undecided voter, but said he would most likely vote for Mr. Romney.

“I’m going to stand here every weekend until Obama’s gone,” said Mr. Triana, sweating in the blistering sun. “My sign was going to be more nasty, but my family said, ‘Somebody’s going to shoot you.’ ”

He continued, “I can’t explain the housing crisis, but I know that if the economy was better, everything would be better.”

In the condominium development where she lives in Homestead, Fla., south of Miami, Patricia Newlan said that 10 of 87 units are in foreclosure, which has driven up maintenance fees for everyone else and caused other problems. “Honestly, I’m not sure what Romney intends to do specifically on that issue, but I’m leaning toward him,” she said. “He comes across as a smart businessman.”

John Briggs, a nuclear plant worker who lives in Islamorada, Fla., agreed, saying: “I would like to hear what his plan is, but he’s had an impressive career. I have more faith in him than the others to turn the economy around.”

Chris Vellanti, who lives in Tampa, is a real estate investor still recovering from the loss of three of his five properties to foreclosure in 2009. “I’m going to vote for Romney by default,” he said. “I’m a product of my environment, being born and raised by staunch Republicans. I’m a believer in laissez-faire. And I’ll take any Republican over Obama.”

Mr. Vellanti continued: “My brother is a Realtor, and I don’t think he’s sold a house in a year. I blame the recession on the Democrats in Congress that wanted everyone to own a home, even if they couldn’t afford it.”

Analysts expect downward pressure on home prices and foreclosures to hamper the Florida real estate market for at least the next two years.

“The fact is that there’s no easy answer, no magic bullet that some candidate is going to think of,” said Brad Hunter, a chief economist for Metrostudy, a firm that analyzes housing and development across the country. “A candidate talking to Floridians is going to be asked, ‘What are you going to do to help us?’ And there’s no easy answer.”

For the moment, Mr. Romney seems to be relying on optimism.

“It will get better,” he said at a round-table discussion on Monday morning in Tampa, speaking to a woman at risk of losing her home. “It won’t always be like this. This is a detour.”