The president's warning on the debt ceiling and Boehner's call to resume direct talks comes 27 days before the country reaches the "cliff" -- a barrage of deep automatic spending cuts and across-the-board tax increases that economists say could cast the economy back into recession.
Seeking to avert a crisis, some Senate Republicans – most recently Olympia Snowe of Maine and Tom Coburn of Oklahoma -- have expressed support for raising tax rates on the nation's top earners in an attempt to break the partisan logjam.
"I know we have to raise revenue," Coburn said on MSNBC. "I don't really care which way we do it."
Democrats pounced on his statement, saying it should "provide cover" for House Republicans to follow suit. But none have so far shown willingness to accept increased rates, prompting Boehner to continue to hold the line.
Despite the urgency, the House of Representatives will conclude legislative business for the week later today, releasing most lawmakers back to their districts for a long weekend.
One person who plans to stay in town, however, is Boehner.
"I'll be here," he told reporters. "I'll be available at any moment to sit down with the president to get serious about solving this problem."
Obama and Boehner have only spoken once in the past week, even though the Speaker attended the White House holiday reception Monday evening.
Obama suggested in an interview Tuesday that he has not met more regularly with Boehner because of their unresolved disagreement on tax rates. Boehner opposes increasing them on any Americans.
"Speaker Boehner and I speak frequently," Obama said. "I don't think the issue right now has to do with sitting in a room.
Obama today continued to express cautious optimism that a deal could be reached but was adamant that it will require higher tax rates on the wealthy to raise $1.6 trillion in new revenue.
"We can probably solve this in about a week. It's not that tough," Obama said. "But we need that conceptual breakthrough that says we need to do a balanced plan; that's what's best for the economy; that's what the American people voted for; that's how we're going to get it done."
Republicans argued that Obama is moving the goal posts on taxes. Last year, he said publicly that $1.2 trillion in new revenue could be raised without raising rates; today, he says, the math doesn't add up.