With the battle for the Repub­lican presidential nomination moved to Florida, the candidates find themselves confronted with a question central to the health of the state’s weak job market: What are their plans for solving the housing mess?

Florida’s economy rests heavily on housing, which has struggled in the years since the bubble burst. New construction has slowed to a crawl and home prices have tumbled, sapping consumer confidence, choking tax revenue and leaving the state with one of the nation’s highest unemployment rates.

President Obama has acknowledged that his housing policies have been ineffective, an assertion vividly illustrated by the many half-built developments and large inventory of financially distressed properties that dot the Florida landscape.

That might sound like a political opportunity for the GOP candidates, particularly in Florida, which is seen as pivotal to their party’s chances to capture the White House. But so far, the candidates have not been specific on how they would address the housing problem.

Visiting the state Monday in advance of the Jan. 31 primary, former Massachusetts governor Mitt Romney staged a housing roundtable with eight Floridians who are struggling with the housing market — either their homes are in foreclosure or their insurance or realty companies are floundering.

Romney listened to their tales of woe, taking notes on a yellow legal pad and interjecting at points to express empathy. “It’s tragic,” he said, adding: “It will not always be like this.”

But he has offered no new proposals. Instead, Romney criticized his top rival, former House speaker Newt Gingrich, for his work as a consultant for mortgage giant Freddie Mac, which netted his firm at least $1.6 million between 1999 and 2008. Gingrich has responded by dismissing his GOP rival as a desperate candidate.

In the years since the crisis took hold, leading GOP economists have proposed that the government back a massive mortgage refinancing program or principal write-downs to help homeowners. But those ideas present a conundrum for Republican candidates who want a smaller government role in the economy. For every voter who might be helped and won over by government help with their mortgages, many other homeowners who struggle to pay their bills are likely to be turned off, analysts say.

“This is truly a no-win situation if you are a Republican candidate,” said Jaret Seiberg, a senior policy analyst with Guggenheim Partners’ Washington Research Group. “Every answer requires more government help. There is no cheap or easy way to fix housing. So from their perspective, you are better off ignoring the problem than trying to put a plan forward.”

Romney’s top economic adviser, R. Glenn Hubbard, has proposed using the government mortgage giants Freddie Mac and Fannie Mae to initiate a large wave of refinancings to help homeowners reduce their mortgage payments.

Hubbard estimates that more than 75 percent of the homeowners with 30-year mortgages backed by Fannie Mae or Freddie Mac are paying interest rates higher than 5 percent, even as prevailing rates have been at or below that level for the past two years. He has said the proposal could bolster the economy by saving homeowners a cumulative $36 billion in mortgage payments, while helping as many as 14 million people.

But Romney has been reluctant to embrace the proposal. His caution, which mirrors that of the other GOP candidates, is well founded, according to political consultants.

As the housing market was collapsing in 2008, GOP presidential nominee Sen. John McCain (Ariz.) proposed having the federal government buy up the bad mortgages and then negotiate new loan terms with homeowners.

The plan, which was estimated to cost $300 billion, was shot down before it could be fully fleshed out, recalled Douglas Holtz-Eakin, who served as McCain’s top economic adviser.

“There was enormous sentiment from people who said, ‘I got a 30-year mortgage and I am not going to pay for somebody who is now in trouble,’ ” Holtz-Eakin said. “There seems to be no large-scale economically feasible housing intervention that is politically feasible.”

Instead of more government help, the GOP candidates have called for an even smaller federal role in housing. They have proposed doing away with Fannie Mae and Freddie Mac, the government-backed financing giants that are virtually propping up the nation’s mortgage market. Despite his past work for Freddie Mac, Gingrich has called for both companies to be broken up and has criticized new financial regulations for discouraging banks from lending.

Gingrich has also called for the repeal of Dodd-Frank, saying that the move would cause the housing market to “start to improve overnight.” The law was intended to prevent the abuses that helped cause the financial crisis. But Gingrich argues that the new rules hamstring banks, discouraging lending.

Yet Fannie and Freddie are central to the government’s response to the housing crisis. Eliminating them— which is also a long-term goal of the Obama administration — is unlikely to be possible anytime soon without making the market worse, experts say.

The ongoing housing problems are impeding the economic recovery across the country. Home prices have fallen by a third from heir 2006 peak, resulting in about $7 trillion in household wealth losses, according to the Federal Reserve.

The problem has hit particularly hard in Sun Belt states such as Nevada, Arizona and Florida, where housing construction played an unusually large role in the boom that came before bust.

The disappearance of housing-related jobs is a big part of the problem in Florida. The state’s unemployment rate stood at 10 percent in November, an improvement over the recent past but far above the national rate of 8.7 percent for that month. The number of construction jobs in the state has plummeted by more than half between July 2006 and last November, leaving more than 350,000 construction workers out of a job.

Few economists imagine all of that economic damage being cleared without a robust recovery in the housing market.

Sales volume in Florida and housing starts are beginning to increase, although median prices are down by as much as 60 percent from their peak. Some estimates place the percentage of mortgage holders who owe more than their homes are worth at 50 percent.

In northeast Florida’s Flagler County, median prices have plunged from $260,000 in June 2008 to $120,000 now, according to Don “Toby” Tobin, who runs a real estate Web site called Go­Toby.com. About half of transactions are distress sales — either foreclosures or short sales. In addition, many buyers are using cash, because home mortgages are hard to come by for people with less-than-perfect credit.

“We have seen a tremendous amount of damage, and it is all on the property-owner level,” Tobin said.

A rapid recovery is not likely, according to analysts. “It is a grim outlook because in most markets there is no prospect of housing prices returning to the unsustainable levels we saw from 2005 to 2007,” said Stan Geberer, senior associate with Fishkind and Associates, an economic forecasting firm in Orlando. “You can save, you can scrimp, you can cut your expenses, you can work a second job, but no matter what you do you are always in deficit. It is demoralizing.”

John Sebree, senior vice president for public policy for Florida Realtors, said he would like to hear the candidates talking more about freeing up lending for credit­worthy borrowers.

“Admittedly, you wouldn’t expect to hear a Republican candidate talking about government housing programs,” he said.