That appeared to be the hope of Boehner and the rest of the leadership, that by showing his rank and file is united behind the fallback bill, the speaker would be in a strong position to demand concessions from the White House in the broader endgame.
Democrats had their own issues, but so far, they have remained largely submerged as Republicans struggle.
Reps. Peter DeFazio of Oregon and Jim McDermott of Washington, both veteran liberals, announced their opposition to a provision that Obama is backing to slow the growth of cost-of-living benefits for Social Security and other benefit programs.
At the White House, Obama repeated that he is ready to agree to spending cuts that may cause distress among some fellow Democrats, but he saved his sharpest words for Republicans.
"Goodness, if this past week has done anything, it should just give us some perspective," he said in a reference to the shootings of school children in Connecticut.
Yet even as he implored Republicans to "take the deal," he made it clear he's open to more bargaining.
Asked whether he might be flexible on the level at which tax rates should rise, he said he wasn't going to bargain in public. He also addressed the issue of politics.
Speaking of Republicans, he said, "It is very hard for them to say yes to me. But at some point, they've got to take me out of it."
He added, "I'm often reminded when I speak to the Republican leadership that the majority of their caucus' membership come from districts that I lost. And so sometimes they may not see an incentive in cooperating with me, in part because they're more concerned about challenges from a tea party candidate, or challenges from the right, and cooperating with me may make them vulnerable."
Nor did Boehner slam the door on further compromises in his brief appearance before reporters. "Republicans continue to work toward avoiding the fiscal cliff," he said.