Updated

He won't be inaugurated until Jan. 20, but for all intents and purposes, Wednesday is Day One of President Obama's second term as he and congressional leaders shift their immediate focus to a crucial lame-duck session.

Together, they face the challenge of dealing with the so-called "fiscal cliff" -- a potentially disastrous mix of massive defense cuts, cuts to social programs and tax hikes set to kick in come January, less than two months from now.

So the big question a day after Obama's decisive electoral-vote victory is, will it be gridlock as usual or did Tuesday night's results herald a new era of compromise? The answer is especially urgent in the face of a policy threat that some economists say could trigger another recession if left un-addressed.

“If there is a mandate, it is a mandate to work together,” House Speaker John Boehner said Wednesday, adding, “2013 will be different.”

The balance of power in Washington was unchanged after Tuesday's results, and leaders in both chambers came out of election night calling for bipartisanship -- but also reaffirming their parties' dueling positions, which so far have prevented any compromise from being reached.

On the expiration of the Bush-era tax rates, Republicans have refused to allow a tax hike on anyone, saying it could harm small businesses, while Democrats have pushed for an increase on households making more than $250,000, or the top 2 percent of incomes.

Boehner said Tuesday night there is "no mandate for raising taxes." He told Fox News earlier that Obama "knows we're not going to raise taxes on American small businesses. He knows it." Boehner predicted a "real brawl" if the president doubles down on that.

However, Fox News' exit polls from Tuesday night, show that only 14 percent of voters said taxes were the biggest economic problem they faced, and 60 percent of voters said they thought taxes should increase for everyone or for just top earners.

Only 35 percent of voters agreed with Republicans that the rates should stay the same for everyone.

Boehner said Wednesday afternoon that he is willing to work with the White House and Democrats in Congress to tackle “massive debt” as well as the looming “fiscal cliff," though he suggested his focus will be on closing tax loopholes more than raising rates.

The speaker said Republicans are open to a blueprint that would involve reforming federal entitlement programs and the tax code to produce more revenues -- without raising tax rates -- because, he insisted, it would costs jobs and hurt the economy. And he said the president would have to “be willing to reduce spending" -- while avoiding the dramatic defense cuts that will kick in automatically in January if Congress doesn't act to stop them.

In the Senate, Majority Leader Harry Reid said Wednesday that "we need to start working together, a lot. Gridlock is not the solution."

Even so, he disputed Boehner's contention that the public doesn't support a tax increase, saying the election was a "mandate ... that the richest of the rich have to help a little bit."

"I'm going to do everything within my power to be as conciliatory as possible. I want to work together, but I want everyone to also understand, you can't push us around," Reid said, adding: "I think we should just roll up our sleeves and get it done."

For his part, Obama made a number of promises for his second term, as he appealed in his victory speech early Wednesday for a meeting of both sides.

“By itself, the recognition that we have common hopes and dreams won’t end all the gridlock or solve all our problems or substitute for the painstaking work of building consensus and making the difficult compromises needed to move this country forward. But that common bond is where we must begin,” he declared.

“I am looking forward to reaching out and working with leaders of both parties to meet the challenges we can only solve together. Reducing our deficit. Reforming our tax code. Fixing our immigration system. Freeing ourselves from foreign oil. We’ve got more work to do.”

His stated to-do list is ambitious – creating a million new manufacturing jobs, lowering tuition for college students, ending subsidies to oil companies and doubling exports. He wants to make sure his so-called ObamaCare law will lower average family premiums and to strengthen Medicare. And with Obama winning Tuesday and the Democrats retaining control of the Senate, the chances of Republicans repealing the law have all but slipped away.

But Obama also could be setting himself up for tough battles with a divided Congress on some issues, including immigration reform and climate change, which he briefly alluded to in his victory speech.

Whether the lame-duck Congress will usher in a new era of cooperation depends on how the parties view the election results. Despite Obama's victory, each party has reason to think their side's position was reinforced. Democrats are set to expand their majority in the Senate, while Republicans could expand theirs in the House.

"It depends on the extent to which congressional leaders worry about the low approval ratings for Congress," said Darrell West, director of the Center for Governance at the Brookings Institution. "If they think that was one of the reasons why Republicans did poorly, then they will be more willing to negotiate. If they think Republicans lost just because Romney was a bad candidate, they will be less likely to compromise."

But he added, "each party has an incentive to negotiate because they both have their political problems." On one hand, the Democrats are often seen as weak on defense and defense industry jobs, which would face nearly $500 billion in cuts alone if so-called sequestration were to go fully into effect. Meanwhile, Republicans have been seen as defending tax cuts, especially for higher-income earners, at all costs.

Candidates on both sides pointed to the "fiscal cliff" as a massive problem created by the other side during the campaigns. But right now it is clearly a shared problem because in addition to the Pentagon cuts, they face the end of last year's temporary payroll tax cuts, which would raise workers' taxes by an estimated 2 percent; an end to the current tax rates instituted by former President George W. Bush, which would mean higher taxes for all, and shifts in the alternative minimum tax that would take a larger bite from a large swath of earners.

Obama and the Democrats have argued for letting the Bush tax rates expire for the top earners, while Republicans have yet to budget on preserving them. Time will tell if there is room for negotiation -- such as through a combination of increased revenue and acceptable spending cuts.

Obama may hold the upper hand. According to some analysts, there might be an equal chance both sides will fail to come to any major agreements, meaning the the lame-duck session will end “lame.” Some have suggested that the Democrats may just let the current tax rates expire in order to be in a better bargaining position come January.

Sequestration may even be on the table, too, with a more amenable fix placating both the defense hawks and those seeking to trim the giant Pentagon budget possible in January. This scenario seems more plausible, as the White House Office of Management and Budget, which would set parameters of the cuts, has suggested they would not be severe in the short-term.

Still, the ideological lines are firm, and with the addition of two fiscal conservatives to the Republican ranks in the Senate -- Ted Cruz from Texas and Jeff Flake in Arizona -- there might be more of a hardening of positions than Hill watchers think, said David Boaz, senior politics analyst from the Cato Institute.

"My gut level instinct would be there are fundamental differences between the Democrats and the Republicans in Congress and the election hasn't moved us any closer to resolving these questions," he said.