The Obama administration is considering further actions to strengthen the housing market, but the bar is high: plans must help a broad swath of homeowners, stimulate the economy and cost next to nothing.

One proposal would allow millions of homeowners with government-backed mortgages to refinance them at today’s lower interest rates, about 4 percent, according to two people briefed on the administration’s discussions who asked not to be identified because they were not allowed to talk about the information.

A wave of refinancing could be a strong stimulus to the economy, because it would lower consumers’ mortgage bills right away and allow them to spend elsewhere. But such a sweeping change could face opposition from the regulator who oversees Fannie Mae and Freddie Mac, and from investors in government-backed mortgage bonds.

Administration officials said on Wednesday that they were weighing a range of proposals, including changes to its previous refinancing programs to increase the number of homeowners taking part. They are also working on a home rental program that would try to shore up housing prices by preventing hundreds of thousands of foreclosed homes from flooding the market. That program is further along — the administration requested ideas for execution from the private sector earlier this month.

But refinancing could have far greater breadth, saving homeowners, by one estimate, $85 billion a year. Despite record low interest rates, many homeowners have been unable to refinance their loans either because they owe more than their houses are now worth or because their credit is tarnished. 

Exactly how a refinancing plan might work is still under discussion. It is unclear, for example, whether people who are delinquent on their mortgages would be eligible or whether lenders would administer it. Federal officials have consistently overestimated the number of households that would be helped by their various housing assistance programs.

A working group of housing experts across several federal agencies could recommend one or both proposals, or come up with new ones. Or it might decide to do nothing.

Investors may suspect a plan is in the works. Fannie and Freddie mortgage bonds had been trading well above their face value because so few people were refinancing, keeping returns on the bonds high. But those bond prices dropped sharply this week.

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