"I still think we can get it done," Obama said as he struggled to pick up the pieces of weeks of failed negotiations and political maneuvering.
The president spoke at the end of a day in which stocks tumbled and congressional leaders squabbled as the fiscal cliff drew implacably closer.
"How we get there, God only knows," said Boehner at a morning news conference, referring to the increasingly tangled attempts to beat the Jan. 1 deadline and head off the perilous combination of across-the-board tax hikes and deep spending cuts that threaten to send the economy into recession.
There was no immediate response from his office to the president's remarks.
Obama spoke shortly before a scheduled departure to join his family in Hawaii for Christmas, but in an indication of the importance of the issue, he told reporters he would be returning to the White House next week.
He said that in his negotiations with Boehner, he had offered to meet Republicans halfway when it came to taxes, and "more than halfway" toward their target for spending cuts.
He said he remains committed to working toward a goal of longer-term deficit reduction, but in the meantime he said politics should not prevent action on legislation to keep taxes from rising for tens of millions.
"Averting this middle class tax hike is not a Democratic responsibility or a Republican responsibility. With their votes, the American people have decided that government is a shared responsibility," he said, referring to a Congress where power is divided between the two parties.
"Everybody's got to live a little bit in a sensible way. We move forward together or we don't move forward at all," he added.
Progress was invisible one day after House Republican rebels thwarted Boehner's plan to prevent tax increases for all but the nation's million-dollar earners. And while neither House is expected to meet again until after Christmas, officials in both parties said there was still time to prevent the changes from kicking in with the new year.
Yet they pointedly disagreed which side needed to make the first move.
Reid said that, for now, Boehner should allow a vote on legislation that would block all tax increases except for individuals making more than $200,000 and couples making $250,000 - the position that Obama carried through his successful campaign for reelection.