The housing market is still a mess, and continues to serve as a drag on the economy. Addressing the problem isn’t exactly easy.

As Ezra Klein explained this morning, federal officials don’t want to simply force the banks to eat homeowners’ debts because it would undermine the industry. They also don’t want to have the government simply eat the losses, because it’d be a political problem — the feds would be “telling the people who are making their mortgage payments that they’re going to have to pay for the people who aren’t making their mortgage payments.”

The Obama administration has a different idea, which has been lingering for a couple of years, but which apparently is starting to gain some traction.

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.

There are apparently other ideas under consideration, but the refinancing approach, the details of which still need to be worked out, would have the biggest bang for the buck: homeowners, many of whom are currently under water, would stand to save $85 billion. They’d still have a mortgage payment to make, but they’d find it easier to afford and would have more money to spend on other things.

Economist Christopher Mayer at the Columbia Business School explained, “This is the best stimulus out there because it doesn’t increase the deficit, it accomplishes monetary policy, and it reduces defaults in housing.”

And what about Congress? That’s probably the best news of all: the administration could act on this without congressional approval.

I’d also note the story behind the story: this NYT story looks an awful lot like a deliberate leak, put out by Obama administration officials, in part as a trial balloon, and in part to signal what’s possible.

It’s something to keep a close eye on.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.