IT’S NO SECRET that President Obama is frustrated by the housing market’s resistance to federal policy solutions. He admitted as much at a Twitter “town hall” last summer. And those remarks were apparently a polite version of the presidential “disappointment” that had already boiled over in a White House meeting with aides in December, according to a front-page story Monday by The Post’s Zachary A. Goldfarb. No doubt the president is right to identify foreclosures and negative home equity as huge drags on the U.S. economy. The problem, though, is that there is no quick fix — short of, perhaps, a mass federal buy-up of underwater mortgages, which would cost hundreds of billions of dollars and trigger a backlash from taxpayers who didn’t get a share of the largess.

So, for all his understandable desire to do more, Mr. Obama has been condemned to trying one incremental approach after another, hoping to hit that policy sweet spot where the government shores up the housing market and the broader economy without doing too much collateral damage to either.

Mr. Obama’s most recent attempt is a plan, unveiled in a Las Vegas speech Monday, to ease refinancing at today’s record low rates for underwater homeowners. To qualify, a borrower must be current on his or her mortgage, which must, in turn, be among those underwritten before June 2009. The mortgages also must have a current loan-to-value ratio greater than 80 percent and be backed by Fannie Mae and Freddie Mac, the mortgage-securitization giants operating under federal control.

The theory here is threefold: First, moral hazard would be at a minimum because the lower-rate loans would be going not to irresponsible borrowers but to people who have kept up their payments; second, there is little increased risk to taxpayers, since Fannie and Freddie already guarantee these loans; and third, reducing these borrowers’ monthly payments would put them at lower risk for foreclosure and increase their propensity to spend at the mall, boosting the economy.

Essentially, it’s a revised version of the Home Affordable Refinancing Program (HARP), which has been in existence since 2009 but has produced fewer than 900,000 refinanced loans so far. The Congressional Budget Office has guesstimated the possible benefits at $7.4 billion in the first year, spread out over 2.9 million households.

Mr. Obama has pushed a plan like this for months, but the regulators who control Fannie and Freddie have resisted. In the regulators’ view, relaxing fees and underwriting criteria would be inconsistent with limiting the enterprises’ losses, which are ultimately charged to taxpayers. Now, regulators and the Obama administration have struck a compromise that cuts fees and reduces certain legal risks to banks that had deterred them from taking part in HARP. These changes could increase participation in the program — though how much, exactly, won’t be known until Fannie and Freddie produce details next month.

This is no free lunch: Whatever additional money households gain would come out of the pockets of investors who hold Fannie and Freddie’s mortgage-backed securities. Nothing illegal about that; they assumed refinancing risk when they bought the bonds. But the investors’ loss of wealth offsets to some degree the hoped-for greater spending by the program’s beneficiaries.

In short, it’s a modest step toward household deleveraging, not a panacea. “Given the magnitude of the housing bubble, and the huge inventory of unsold homes . . . it will take time to solve these challenges,” Mr. Obama acknowledged Monday. Frustrating but true.