Boehner's leverage in negotiating a deal got weakened by the election that returned Obama to the White House, broadened the Democratic majority in the Senate and slightly narrowed the Republican majority in the House.
While the election resulted in another split Congress like the current session that has become a symbol of legislative dysfunction, both sides have signaled a possible new openness to an agreement that was unreachable in the past two years.
In the final days of the campaign, Vice President Joe Biden referred to private talks with members of Congress on the pending fiscal impacts of expiring tax cuts and mandatory budget cuts. This week, Boehner called on Obama to work with him to complete a comprehensive deficit reduction agreement -- the "grand bargain" that eluded them last year.
Both Boehner and Obama were held back from a deal back then because of pressure from their respective bases, retiring Republican Rep. Steve LaTourette of Ohio told CNN.
"The 'no-tax pledge' people in the Republican Party yanked Boehner back and the 'don't you dare touch the middle class' entitlement people in the president's party pulled him back, and as a result those talks collapsed," LaTourette said.
Boehner said this week that a comprehensive agreement won't happen by the end of the year in the lame-duck session of Congress. He proposed that the two sides use that time to set up a framework for substantive negotiations when the new Congress comes in next year while taking short-term steps to avoid the fiscal cliff.
Durbin, the No. 2 Democrat in the chamber, said such a timetable could work.
"We have a chance in the lame duck to at least start the process, and I think there's a chance to rally bipartisan support," he said. "These are basic issues we can work out, and the president is in a position to do that."
Both sides agree the best outcome would be a broad deal addressing the overall need for deficit reduction, including reforms to the tax system and entitlement programs such as Social Security, Medicare and Medicaid.
However, they remain far apart on exactly how to forge such an agreement.
Obama campaigned on having wealthy Americans contribute more to deficit reduction efforts, and White House spokesman Jay Carney said Friday that the president will veto any package that extends the Bush tax cuts for income over $250,000.
"We can't just cut our way to prosperity," Obama said Friday. "If we're serious about reducing the deficit, we have to combine spending cuts with revenue and that means asking the wealthiest Americans to pay a little more in taxes."
Boehner and Republicans oppose raising taxes on anyone, and instead back a broad reform of the tax system that would lower rates further for everyone while eliminating some deductions and loopholes.
While Boehner said this week that his side was open to increasing revenue from such reforms, he made clear that such increases should come from resulting economic growth instead of higher tax rates.
In essence, Boehner proposed the kind of tax reform championed by failed Republican presidential challenger Mitt Romney, whose plan was criticized by Obama and many economists for being unrealistic in assuming that the combination of closed loopholes and economic growth would equal the lost revenue of tax cuts.
Obama's victory gives him new leverage in the budget battles after Republicans forced the president and Democrats into prolonged and sometimes bitter showdowns in the last two years.
One top Democrat with close ties to leaders on Capitol Hill and the White House said that the imminent expiration of the Bush tax cuts means Obama "doesn't have to do anything and everyone's taxes go up," which is a GOP nightmare.
Such an increase would affect personal income tax, the estate tax, dividends and capital gains taxes.
In addition, some officials are hinting the feared sequester cuts don't have to be implemented right away in the new year, giving at least a few months for a deal to be worked out.