Another conservative leader, Brent Bozell, chairman of the group ForAmerica, urged lawmakers not to trust a deal that, in his words, "was brokered behind closed doors."
"No deal is better than a bad deal," Bozell said. "The Republicans will be in a much stronger position in just a few weeks when they can revisit this and get a better deal for the American people."
Increasingly, groups to the left of Obama are questioning the president's resolve.
Adam Green, co-founder of the Progressive Change Campaign Committee and a leading progressive critic of the administration, accused Obama of "undercutting his 'yes we can' mantra," and acceding to GOP demands without putting up a fight.
"He telegraphed his willingness to cave from the start by solely talking about 'compromise' and never talking about holding Republicans accountable to their constituents if they opposed him," Green said. "He has zero standing to say he tried to persuade Senate Republicans and zero standing to ask millions of his former supporters to support an incompetently negotiated deal."
Supporters of Green's group, as well as other left-leaning advocacy organizations like MoveOn and Democracy For America, led a charge this week to persuade members of Congress to sign on to a letter spearheaded by Rep. Peter Welch, D-Vt., urging fellow lawmakers to oppose the tax deal.
The White House has not taken these knocks lying down. It has launched an aggressive persuasion campaign of its own, unveiling endorsements from more than three dozen senators, governors and even mayors. Administration officials, including economic advisers Larry Summers and Austan Goolsbee, have been deployed to "educate" the public and reluctant members of Congress on the plan.
Now, Democratic leaders want to go back to the drawing board.
"We will continue discussions with the president and our Democratic and Republican colleagues in the days ahead to improve the proposal before it comes to the House floor for a vote," House Speaker Nancy Pelosi said in a statement on Thursday.
Once again, White House officials are negotiating a precarious middle ground.
"If everybody took out what they didn't like," press secretary Robert Gibbs said on Thursday, "we would have nothing. And we know the consequences of doing nothing."