Rep. Barney Frank, D-Mass., predicted the tax cut compromise "will be passed by virtually all the Republicans and a minority of Democrats." He said he would vote against it.
Obama said more congressional Democrats would climb aboard as they studied details of the $900 billion year-end measure.
Raising the direst alarm yet, his administration warned fellow Democrats on Wednesday that if they defeat the plan, they could jolt the nation back into recession.
Larry Summers, Obama's chief economic adviser, told reporters that if the measure isn't passed soon, it will "materially increase the risk the economy would stall out and we would have a double-dip" recession. That put the White House in the unusual position of warning its own party's lawmakers they could be to blame for calamitous consequences if they go against the president.
With many House and Senate Republicans signaling their approval of the tax cut plan, the White House's comments were aimed mainly at House Democrats who feel Obama went too far in yielding to Republicans' demands for continued income tax cuts and lower estate taxes for the wealthy.
Obama says the compromise was necessary because Republicans were prepared to let everyone's taxes rise and to block the extension of unemployment benefits for jobless Americans if they didn't get much of what they wanted.
Economists say the recent recession officially ended in June 2009. But with unemployment at 9.8 percent, millions remain out of work or fearful of losing ground economically, and the notion of the nation falling back into a recession would strike many as chilling. It also could rattle markets and investors.
The deal Obama crafted with Senate Republican leaders would prevent the scheduled Dec. 31 expiration of all the Bush administration's tax cuts enacted in 2001 and 2003, even though Obama had often promised to end the cuts for the highest earners.
House Democrats, who will lose their majority in January, still hold a 255-179 edge in the current Congress. To pass a big bill with mostly Republican votes would mark a dramatic departure from recent battles, such as the health care overhaul, which was enacted with virtually no GOP support in either chamber.
Passage of Obama's plan seems more assured in the Senate, where numerous Democrats have agreed that the president had little choice in making the compromises with Republicans. Still, Majority Leader Harry Reid, D-Nev., said he and colleagues are considering possible changes, and action could come within days.
- Read 10 Things You Didn't Know About the Bush Tax Cuts.
- Read more about the deficit and national debt.
- Check out a roundup of political cartoons on Democrats.