“The ideal version of housing finance reform is one in which we are clear about what’s worked in the current system and what needs to be overhauled,” Mr. Parrott said. What you want to avoid, he continued, “is a market duopoly that’s got an implied government guarantee. It creates such a toxic mix of incentives where profit-seeking shareholders maximize risk and profit at the expense of taxpayers sitting there waiting to hold the bag if the thing goes south.”

But bringing private capital into the mortgage securities market poses perils of its own, other housing experts say: Allowing too-big-to-fail banks to dominate the nation’s mortgage market would crowd out smaller lenders and expand the federal safety net, putting taxpayers at greater risk of funding bailouts in a downturn. Relying on mortgage insurers to provide that capital also seems dubious given how badly these companies performed in the 2008 crisis.

Moreover, private capital would probably flee the mortgage market at the first sign of trouble, as it did during the recent credit debacle. This raises questions about the availability of home lending when such a system goes through a rough patch.

Lost in the debate over the future of Fannie and Freddie is the role Congress had in mind for the F.H.F.A. when it passed the Housing and Economic Recovery Act of 2008. Under the law, a conservator is supposed to put the regulated entities in a “sound and solvent condition” and “preserve and conserve” their assets and property.

Proponents of eliminating Fannie and Freddie say that allowing them to survive would also mean letting them go back to their abusive ways. The companies were a huge source of capital for reckless loan products, in Mr. Stevens’s view. “We risk going back to that system,” he said, because the public cannot count on regulators “to protect us going forward and constrain these guys.”

But those who favor recapitalizing the companies — a group that includes hedge funds and other speculators that stand to gain, as well as supporters of low-income housing — say that the past need not be prologue. They contend that the companies could be restructured in a way that would prohibit dubious activities, and that allowing Fannie and Freddie to rebuild capital would reduce taxpayer risk.

The banks are continuing their push for access to Fannie and Freddie’s assets and profits. But they are not putting all their eggs in the legislative basket. In recent months, they have urged Melvin L. Watt, director of the F.H.F.A., to put at least some of their recommendations in place administratively.