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.
In the talks to date, Obama is now seeking $1.2 trillion in higher tax revenue, down from the $1.6 trillion he initially sought. He also has softened his demand for higher tax rates on household incomes so they would apply to incomes over $400,000 instead of the $250,000 he cited during his successful campaign for a new term.
He also has offered more than $800 billion in spending cuts over a decade, half of it from Medicare and Medicaid, $200 million farm and other benefit programs, $100 billion from defense and $100 billion from a broad swath of government accounts ranging from parks to transportation and education.
In a key concession to Republicans, the president also has agreed to slow the rise in cost-of-living-increases in Social Security and other benefit programs, at a savings estimated at about $130 billion over a decade.
By contrast, Boehner's most recent offer allowed for $1 trillion in higher taxes over a decade, with higher rates for annual incomes over $1 million. He's also seeking about $1.3 trillion in spending cuts.
The two sides disagree, too, over increases in the government's debt limit, which will soon need to be raised when borrowing reaches the current $16.4 trillion cap.
Also at issue are unemployment benefits, which are scheduled to expire for an estimated 2 million out-of-work Americans at year's end, and the prospect of reduced payments beginning Jan. 1 for doctors who care for Medicare patients.
Associated Press writers Andrew Taylor, Jim Kuhnhenn, Andrew Miga and Alan Fram contributed to this report.