Obama and Boehner have been quickening talks to reach an agreement. Both met privately at the White House on Monday and also spoke later by phone. Aides to both men would not say whether other meetings were planned but that channels of communication remained open.
The progress, while substantive, renewed questions about whether rank-and-file members of Congress in both parties would back the compromises their leaders were prepared to make.
Some Democrats raised concerns about future limits on entitlement benefits, while several Republicans publicly said they wouldn't support any deal that raised taxes one cent.
"Reducing cost of living adjustments is a Social Security benefit cut. Any deal that cuts Social Security, Medicare or Medicaid benefits is unacceptable, and I will oppose it," said Rep. Charles Rangel, D-N.Y.
The latest ABC News/Washington Post poll shows that most Americans still approve of Obama's handling of the negotiations and would blame Republicans if the country goes over the "cliff." Forty-five percent of Americans approve of Obama in the fiscal talks, with 43 percent disapproving. Congressional Republican leaders hold just 26 percent approval and 65 percent disapproval in the same poll.
The poll also found, however, that Americans by a 56-34 percent margin believe Obama does not have "a mandate to carry out the agenda he presented during the presidential campaign" and that he should "compromise on things the Republicans strongly oppose."
This story has been updated.