"I'll say no, because the focus has got to be on economic growth," said Rep. Jim Jordan, R-Ohio. "The simple fact is raising taxes is not going to grow our economy."
Others wouldn't rule it out completely.
"If there's real cuts in spending, if there's real reform of entitlement programs, I think all of us would have to reconsider our position," Rep. Raul Labrador, R-Idaho, said Wednesday. "But the problem is, I don't see real cuts, real cuts. I'm not saying yes and I'm not saying no."
Liberal Democrats are trying to pull Obama in the opposite direction on Medicare and Social Security. Eighteen months ago, Obama had all but agreed to an increase in the retirement age and a less generous inflation adjustment for calculating Social Security COLAs.
House Minority Leader Nancy Pelosi warned Republicans against insisting on raising the Medicare eligibility age as part of any deal.
"Don't go there," Pelosi said on "CBS This Morning." She said raising the retirement age wouldn't contribute much savings toward an agreement in the short term, adding, "Is it just a trophy that the Republicans want to take home?"
Raising the Medicare age from 65 to 67 could cut Medicare costs by $162 billion over a decade, according to a Congressional Budget Office estimate last year. But by 2035, it would cut Medicare's projected budget by 7 percent.
That estimate, however, assumes the eligibility age would increase rather abruptly and hit people just about to retire. Republicans have instead in the past that their Medicare proposals won't affect now those 55 and above.
Democrats are also pushing back against a GOP plan to reduce Social Security cost-of-living adjustments, another step back from where Obama and Boehner were just 18 months ago.
"Quite frankly, Social Security is off the table," said Rep. Joe Crowley, D-N.Y.
The backtracking has Republicans fuming that Obama campaigned on a "balanced" fiscal solution but now is unwilling to pair tax increases with politically painful cuts to Medicare and other popular programs.
"The president and his allies have taken so many things off the table the only thing left is the varnish," said Senate Minority Leader Mitch McConnell, R-Ky.
But in an ABC interview Tuesday, Obama did not reject a Republican call to raise the age of Medicare eligibility from 65 to 67. The proposal is "something that's been floated," Obama said, not mentioning that he had tacitly agreed to it in the deficit-reduction talks with Boehner more than a year ago that ended in failure.
"When you look at the evidence, it's not clear that it actually saves a lot of money," Obama said. "But what I've said is, let's look at every avenue, because what is true is we need to strengthen Social Security, we need to strengthen Medicare for future generations, the current path is not sustainable because we've got an aging population and health care costs are shooting up so quickly."
Associated Press writers Alan Fram and Nyia Hawkins contributed to this report.