President Obama on Wednesday made his latest pitch to lift the nation’s beleaguered housing market, unveiling a series of proposals to help struggling borrowers reduce their monthly payments and to stem the continuing slide in real estate prices.

The centerpiece of the effort is legislation that would make it easier for homeowners who have been paying their mortgages on time to take advantage of today’s ultra-low interest rates, perhaps saving thousands of dollars a year. Millions of homeowners, including many who owe more than their properties are worth, have been unable to refinance.

White House officials estimated that the proposal, which requires congressional approval, would cost taxpayers between $5 billion and $10 billion. To offset that cost, Obama reprised his previous idea of imposing a new tax on the profits of financial firms. Republicans pledged to oppose the proposal.

To help the economy get more of a boost from low interest rates, Obama proposed that almost anyone who has a credit score above 580 and has been paying his or her monthly mortgage bill on time for the past six months be able to refinance. It wouldn’t matter under Obama’s proposal whether borrowers had government-backed mortgages or loans owned by banks and other private investors.

The only major limitation to the program would be on borrowers who own very expensive properties, relative to where they live. The maximums range from $271,050 to $729,750. A new program run by the Federal Housing Administration would be set up to refinance mortgages that are not backed by federal mortgage giants Fannie Mae or Freddie Mac.

The proposals are the latest in a long list of programs Obama has unveiled to address the problems facing homeowners. Almost all of the programs have fallen far short of their goals. Obama has acknowledged that his response to the housing crisis has not worked as well as he had hoped it would, and most economists say that the depressed housing market is one of the biggest drags on the economic recovery.

Still, Obama’s continuing push to provide aid to homeowners and boost housing prices draws a stark contrast with Republican presidential front-runner Mitt Romney, who has advocated a hands-off approach to the nation’s foreclosure epidemic. Obama, in his remarks, pointed to areas hit hard by the foreclosure crisis, including Las Vegas in the political battleground state of Nevada, where the next Republican presidential caucuses will take place.

“It will take more time than any of us would like for the housing market to recover from this crisis,” Obama said Wednesday at the James Lee Community Center in Falls Church. “But it is wrong for anybody to suggest that the only option for struggling, responsible homeowners is to sit and wait for the housing market to hit bottom.”

On Tuesday, new data from Standard & Poor’s showed that housing prices have fallen to levels not seen since 2003.

Republicans on Capitol Hill gave the president’s proposal a chilly reception.

“We have done this at least four times, where there is some government program to help homeowners who had trouble with their mortgages,” House Speaker John A. Boehner (R-Ohio) said. “None of these programs have worked and I don’t know why anyone would think this next idea would work.”

At the start of his term, Obama promised that up to 9 million homeowners at risk of foreclosure would receive aid through a broad refinance program or a mortgage modification program run through the Treasury Department. In the three years since then, fewer than 2 million have been helped.

“I’ll be honest — it didn’t work at the scale we’d hoped,” Obama said Wednesday. “Mortgage rates are as low as they’ve been in half a century, and when that happens, homeowners usually flock to refinance their mortgages. But this time, too many families haven’t been able to take advantage of the low rates.”

As part of his new plan, Obama also proposed encouraging borrowers who refinance their mortgages to take on shorter-term loans and direct the savings to rebuilding equity in their homes. As an incentive, the administration is willing to have the government pay the closing costs associated with refinancing — usually about $3,000.

The number of borrowers who might be eligible for the program is large: 3.5 million who do not have federally backed mortgages and 11 million who hold government-backed loans, according to administration officials. But previous estimates suggest that just a fraction of that population would take part in the program.

Christopher Mayer, an economics professor at Columbia who has gained attention for his mortgage proposals, said he’s “a big fan of what the president has proposed for refinancing government-guaranteed mortgages. . . . The program really says for the first time everybody is eligible.”

But he raised concerns about the new FHA program that would refinance mortgages not already owned by the government. “I think it is taking a lot of risk for the government, and I think taxpayers have a legitimate question of whether they have already taken on a lot of risk,” he said.

Other steps announced Wednesday include a decision by the Treasury Department to triple incentives paid to banks in exchange for forgiving part of the debts owed by homeowners, as well as a program run by the Federal Housing Finance Agency to sell batches of foreclosed properties to investors, who would rent them out. That could restart housing activity and put a floor under housing prices in struggling communities.

Staff writer Brady Dennis contributed to this article.