What’s he talking about? As the Wall Street Journal’s Nick Timiraos reports, the White House is pushing for changes to an existing program, the Home Affordable Refinance Program (HARP), which allows borrowers with loans guaranteed by Fannie Mae and Freddie Mac to refinance their mortgages. Right now, rates on 30-year fixed mortgages are at 4.12 percent, their lowest level in half a century, so letting homeowners refinance could put a lot of money in their pockets.

Most conveniently, from the White House’s perspective, this plan doesn’t need approval by Congress. It just needs buy-in from the Federal Housing Finance Agency. True, as Ezra and I have reported, the FHFA hasn’t always been kind to Obama’s housing initiatives, but the agency does seem tentatively receptive to this idea. That said, previous plans to allow refinancing—including HARP itself—haven’t worked very well. Why should this time be any different?

For a sense for whether a refinancing scheme could actually help the economy, here’s a new analysis from the Congressional Budget Office. This isn’t an official estimate, since there’s no official plan yet. Instead, CBO’s economists invented their own (plausible-sounding) refinancing scheme. Their plan would be available for one year and allow borrowers who aren’t behind on their mortgage to refinance at current market rates. One key point is that borrowers wouldn’t have to pay the large risk-based fees often demanded by Freddie and Fannie, which deter many people from refinancing—the fee would just be the one paid on the initial mortgage.

Here’s what the CBO predicts the results would be: About 2.9 million homeowners would take the government up on its offer, saving $7.4 billion in lower monthly payments in the first year alone. An additional 111,000 borrowers would avoid default, which would, in itself, save Fannie Mae and Freddie Mac—and hence taxpayers—$3.9 billion.

Against that, however, government investors in mortgage-backed securities—including Treasury, the Federal Reserve, Fannie, and Freddie—would lose about $4.5 billion, as loans get paid off early. So the net cost to the government would be pretty modest. Private investors in mortgage-backed securities, meanwhile— a group that includes banks, pension funds, mutual funds, etc.—would take a hit of about $13 billion to $15 billion.

Now, since many of these investors are foreign, and since these investors wouldn’t all necessarily reduce spending by the amount of their losses, the CBO estimates that the “net effect would be an economic stimulus” for the U.S. economy. The money gained by borrowers does more to boost the economy than the money lost by investors.

Granted, this plan is very far from a panacea for U.S. housing woes. The CBO notes that the “gains and losses are small relative to the size of the housing market, the mortgage market, and the economy.” What’s more, the plan does nothing to help borrowers who are already in default or whose mortgages are so deep underwater that refinancing is all but impossible.

Still, when it comes to plans that are politically feasible, this is one option. There are still hurdles: The Obama administration will need to convince the banks that originated many of these mortgages to participate in the plan. As Bloomberg reported in August, HARP has only helped 810,000 homeowners to date, far lower than the original goal of 5 million, because lenders are worried that they’ll be forced to buy back mortgages that go into default soon after refinancing. And the White House will have to convince the FHFA to let Fannie and Freddie take on additional risk (which means additional risk to taxpayers). None of those steps is easy. But relatively speaking, it might be less daunting than squeezing a bill through Congress.