In the event both sides cannot reach a broad deal, there is still some optimism about a last-ditch effort by both parties to prevent an income tax hike on 98 percent of earners.
The Senate has already passed a measure extending tax rates for families earning $250,000 a year or less. The House could decide to act on that, and nothing more, if the impasse reaches the 11th hour.
The latest ABC News-Washington Post poll shows more Americans back Obama over Boehner in the budget talks by a 2-to-1 margin. But the numbers are hardly overwhelming.
Forty-nine percent approve of Obama's handling of the "fiscal cliff," while 42 percent disapprove. Just 25 percent approve of Boehner's handling of the situation, although that is at least in part because many more people are in the dark about his efforts, according to the poll.
ABC News' Jonathan Karl contributed reporting.