The Senate Banking Committee on Tuesday delayed consideration of a measure that would revamp the nation’s housing finance system, with the panel’s leaders signaling that they have enough votes to pass the bill out of committee but not to propel it to the Senate floor.

The legislation, offered by Sens. Tim Johnson (D-S.D.) and Mike Crapo (R-Idaho), would dismantle mortgage giants Fannie Mae and Freddie Mac and shift most of the risk of mortgage lending to the private sector. The bill’s supporters often cast the measure as the last major piece of reform left to tackle following the 2008 financial crisis.

On the 22-member committee, six Democrats and six Republicans support the measure. The panel’s leaders delayed the vote in hopes of securing a larger majority by winning over more liberal Democrats, according to Capitol Hill aides who are not authorized to speak publicly about the negotiations. The goal is to have a broad coalition behind the bill so that Senate Majority Leader Harry M. Reid (D-Nev.) feels compelled to move it to the full chamber.

The liberal faction — including Sens. Charles E. Schumer of New York, Elizabeth Warren of Massachusetts and Robert Menendez of New Jersey — was making little headway, Democratic aides said, adding that the two sides remained far apart on an array of issues.

Those lawmakers are concerned that the bill gives big banks too much control of the mortgage industry, does not do enough to encourage lending in underserved areas and could lead to far more expensive mortgages for borrowers. Some of the lawmakers represent pricey housing markets and are pushing to raise the ceilings on mortgages that Fannie and Freddie will back in their states.

While some of the bill’s supporters say they’re confident they can make enough tweaks to satisfy those in the “maybe” column, others are less sure. It’s also unclear whether Reid will be swayed no matter how large the committee’s margin of support, given the distractions of the midterm elections in November.

As each day passes without a committee vote, the chances of getting the bill to the Senate floor this year fade, senior Democratic aides said. Johnson, the committee’s chairman, said in a brief statement that the panel would reconvene “in the coming days.”

“There continue to be important discussions to build a larger coalition supporting the bill,” Johnson said. “While we have the votes to report the bill out today, Members of the Committee have asked for a brief delay to work out additional issues prior to a final vote.”

Meanwhile, coalitions continue to form outside Congress to derail the bill.

On Tuesday, a coalition of business and civil rights groups launched United for American Homeownership to advocate for preserving Fannie and Freddie.

Among its members are the National Consumers League and the National Black Chamber of Commerce. The group is bankrolled by the mutual fund Fairholme Capital Management, which is suing the government over its handling of Fannie and Freddie’s profits. Former Democratic senator Bob Kerrey of Nebraska serves on the group’s board.