HOUSING IS where the Great Recession began, yet Congress and President Obama still haven’t untangled the complex ties among government, business and home buyers that fed into that economic calamity. After five years, though, there is movement toward reforming a big part of the system.

At the moment, the market for new mortgages is almost entirely government-backed through Fannie Mae, Freddie Mac or the Federal Housing Administration. In Phoenix on Tuesday, Mr. Obama rightly argued that the situation must change, that private finance should again be the “backbone” of the system. He supported slowly but steadily winding down Fannie and Freddie, so-called government-backed enterprises meant to drive investment to mortgages, and replacing them with a more modest government role in the market.

Simply hearing the president argue for ending Fannie and Freddie is important. Sen. Bob Corker (R-Tenn.), a major advocate for a bipartisan restructuring plan, said his office saw a wave of interest in reform from other lawmakers following Mr. Obama’s speech. Members of both houses of Congress had already been working on proposals. With both political branches engaged in good faith, there is a real chance something will pass in the next few months.

There are big disagreements to be bridged, though, particularly about what Congress should replace Fannie and Freddie with — if anything. The president signaled support for a Senate plan on which Mr. Corker has been working with Sen. Mark R. Warner (D-Va.). They would create an entity that would provide mortgage insurance for a fee and require mortgage investors to put a significant amount of their own money on the line to get that government backstop. These measures are designed to protect taxpayers from having to provide a massive bailout of the mortgage market.

A bill working its way through the House, on the other hand, would replace Fannie and Freddie with almost nothing. The feds would do little more than monitor the integrity of mortgages bundled into securities and then sold. The House bill would return housing finance to private investors and reduce the distorting effects of extensive federal involvement. But critics worry that the House plan might eliminate the availability of 30-year, fixed-rate mortgages.

The House’s ambitious bill isn’t as likely as the Senate’s to attract enough support to pass Congress and reach the president’s desk. But in pushing for the Senate plan, Mr. Obama must be sure to avoid a political risk of another kind that it poses. There will be strong pressure to reduce the capital requirements for investors to obtain federal backing. Those and other crucial protections for taxpayers must survive intact. A modest federal role may be justified, both politically and on the merits. But the country can’t return to an era in which taxpayers bore the risks of mortgage finance while private entities enjoyed the profit.