Washington is sitting on nearly a third of the nation’s 800,000 repossessed houses, making the U.S. taxpayer the largest owner of foreclosed properties. With even more homes moving toward default, Fannie Mae, Freddie Mac and the Federal Housing Administration are looking for a way to unload them without swamping the already depressed real estate market.

Trouble is, they haven’t figured out how to do that. The government admitted as much in August, when Fannie, Freddie and FHA issued a joint plea to the public for ideas about how to solve the problem. (Give it your best shot: You have until Sept. 15 to email ideas to [email protected]) “They’re stuck,” says Karen Shaw Petrou, managing partner of Federal Financial Analytics, a Washington-based consultant that advises banks and other clients on government policy. “They don’t know what to do.”…

“It isn’t necessarily our preference that FHA is going to itself continue to hold these properties,” says FHA Acting Commissioner Carol Galante. “We want to move homes through the system so we can recover.” The agency has to be careful as it goes, she says. “If you’re putting too much through that system you are helping to drive down prices.” That’s especially true in regions congested with government properties.