WASHINGTON – The Obama administration worked furiously Wednesday to cobble together an unusual coalition of Republicans and centrist Democrats in both houses of Congress as its best bet to win enactment of its tax-cut deal.

Democratic liberals, who dominate the party, remained angry at extending tax reductions for the wealthy. However, prospects that the administration’s strange-bedfellows coalition would prevail appeared good, but fragile.

“I’m afraid they do have the votes,” said Rep. Barney Frank, D-Mass., a veteran liberal.

One development that could make the White House’s task easier would be the support of House Speaker Nancy Pelosi, D-Calif., a champion of the liberal bloc. She’s been highly critical of the tax benefits for the wealthy, but she hasn’t yet said how she’ll come down on the overall plan.

The administration is fighting to extend all Bush-era tax cuts for two years, though President Obama and Democratic liberals had wanted to continue only the reductions for families that earn less than $250,000 annually. All the cuts expire Dec. 31.

The plan also would provide funding for extended jobless benefits, which expired last week, for 13 months, cut payroll taxes from 6.2 percent to 4.2 percent for one year and impose an unusually low 35 percent tax on individual estates of more than $5 million.

Democratic senators emerging from a lengthy meeting with administration officials Wednesday suggested that some changes could be made to the plan, but no major revisions appeared imminent. It wasn’t clear what changes could be made to mollify the liberals without losing GOP support.

The still-unwritten legislation is expected to move first through the Senate, where at least 39 of the 42 Republicans, independent Joe Lieberman of Connecticut and at least seven moderate Democrats are viewed as sympathetic to extending all the rates. Debate could begin today.

“The president has done what he had to do,” said Senate Budget Committee Chairman Kent Conrad, D-N.D. Webb called the package “the ultimate stimulus plan.”

White House economic adviser Larry Summers warned that if Congress fails to pass the compromise, and the tax cuts expire and jobless benefits lapse, it “would materially increase the risk that the economy would stall out and that we would have a double-dip” recession.

The administration’s bigger challenge looms in the House. Though Democrats control 255 of the 435 seats for about another month, the liberals who dominate the caucus have been sharply critical.

“The Republicans successfully held unemployed Americans hostage to give even more tax cuts to millionaires and billionaires. This plan is irresponsible, and I will oppose it,” said Rep. Betty McCollum, D-Minn., a member of the Budget and Appropriations committees.

If all 179 House Republicans support the package — still no certainty — 39 Democrats would need to join them to form a majority.

The Obama-GOP deal would add more than $900 billion to the deficit over two years.