It's been more than five years since the giant mortgage businesses Fannie Mae and Freddie Mac succumbed to the financial crisis and were bailed out by the federal government. But even as they accrue huge profits amid an improving housing market, there's no end in sight for the government's management of the two companies.

Both parties, as well as housing businesses, agree that Fannie and Freddie cannot return to the way they were and that they need to be shut down. But there's no agreement about what should happen next.

“The housing recovery is being impeded by the fact that the system as a whole is in limbo because they’re in limbo,” said Gerald Howard, CEO of the National Association of Home Builders.

But the political and economic stakes are too high to find an easy resolution. In particular, it’s far from clear how Congress would design a system that would wind down the government-sponsored enterprises (GSEs) while ensuring that 30-year, fixed-rate mortgages remained widely available without placing taxpayers at risk for another bailout. Fannie and Freddie don’t issue mortgages, but buy them from lenders, insure them, and package them into securities to sell to investors. They own or guarantee almost two-thirds of all new U.S. home loans.

House Republicans have proposed a measure to limit the government's role in mortgage finance and guard against bailouts, but it is disliked by housing advocates as well as homebuilders. It faces long odds in the House, and even longer in the Democratic-led Senate.

Meanwhile, members of the Senate Banking Committee have been working for nearly a year on a bipartisan bill authored by Sens. Bob Corker, R-Tenn., and Mark Warner, D-Va., to replace Fannie and Freddie with a new Federal Mortgage Insurance Corporation that would provide a narrower government backstop for mortgages. Committee Chairman Tim Johnson, D-N.D., and ranking Republican Mike Crapo of Idaho are deep in negotiations on their own legislation, which is expected to be similar.

Obama has signaled tentative support for the Corker-Warner approach. But it differs so much from the House Republicans' measure that the issue probably won't be resolved without stronger congressional control from one party.

A realistic timeline would have reform legislation passing after Obama leaves office. Bills on this scale "are drafted four, five years before they’re enacted," said Sham Manglik, a housing analyst for the National Low Income Housing Coalition.

In the meantime, however, there are decisions regarding Fannie and Freddie that can’t wait.

One is whether to continue tightening the GSEs' conditions for backing loans, and in so doing cede market share to the private sector. It’s not clear what Mel Watt, Obama’s newly installed director of the Federal Housing Finance Agency that controls Fannie and Freddie, plans to do. Watt, a Democrat, may act instead to expand GSE loans in order to promote affordability.

Another is how to respond to the investors who have taken an interest in Fannie and Freddie’s business.

Fairholme Capital, a hedge fund run by the activist investor Bruce Berkowitz, submitted a plan in the fall to take over the GSEs’ mortgage insurance businesses, saying that it was responding to politicians’ calls for an enhanced role for private capital in housing finance.

Republicans and Democrats dismissed the plan, saying they didn’t want to go back to the bad old days of private companies working for public purposes, risking bailouts. But such arrangements will seem more plausible as Fannie and Freddie languish in the government’s possession.

A group of hedge funds that invested in the GSEs' stocks following the crisis have sued the federal government for deciding in 2012 that it would make a “full sweep” of Fannie and Freddie's profits. Since then, the Treasury, which bailed out the companies to the tune of $187.5 billion, has recouped $185.2 billion, and stands to make a lot more.

However the hedge funds’ efforts pan out, the reality is clear: Fannie and Freddie are in an unsustainable situation that’s only going to become more politically fraught over the next few years.