For the good of the country. Or, this being Washington, the good of their party and their political survival.
The nation's dreaded gridlock is still a four-way intersection in which all the drivers think they have the right of way.
A re-elected president says he has a mandate to raise taxes on the rich. The Republicans running the House say they have mandate to stop tax hikes on anyone. The Democrats who lead the Senate say the election only strengthened their stand, but Senate Republicans still have enough votes to block what they don't like.
In the hours after the election, at least, Republicans and Democratic leaders said they are willing to steer toward compromise, as messy as it may be.
Each side is assessing why and when to give ground in order to get business done, first on fiscal matters, and then perhaps on immigration laws.
The White House in particular was waiting to see the next move from a Republican Party that lost not just the White House race but a little ground in the House and Senate. As Sen. John Cornyn of Texas put it: "We have a period of reflection and recalibration ahead for the Republican Party."
A look inside each camp's political calculus shows voters may see some results.
To start, the Congress and Obama must act because they have created themselves a mess. Nothing big in Washington gets done without a punishing deadline.
Thanks to a series of deals and blown deadlines over the years, the nation on Jan. 1 is due to be hit with tax increases on millions of Americans, plus spending cuts that all sides agree would undermine the military and other basic government functions. The combined hit could throw the economy into recession.
To avoid that, the leaders are talking anew of a grand deal, not a quick fix. As envisioned, it would head off not just the looming fiscal cliff but also open the door for a serious look at reforming the nation's system of taxation and making cost-saving reforms to sacred entitlement programs such as Medicare.
House Speaker John Boehner offered an opening to Obama on Wednesday. "Let's rise about the dysfunction and do the right thing together," he said.
Of course, Boehner and Obama famously fell flat when they reached for such a bargain in 2011, as the country careened toward a perilous default. Boehner said Obama changed the terms, while the White House groused Boehner could not corral House Republicans who did not want to hand Obama a victory before his re-election bid.
"It's not gravy anymore. It's not optional," said Jim Papa of Global Strategy Group, who used to work in the Obama White House legislative office as well as for Democrats in the House and Senate. "It's viewed as something that must get done for the future of the country. So all that's left is to figure out how to do it. And that's what different from last time."
Yet a conflict remains that goes to the core of the fight—indeed, to the core of the election.
Obama insists he will not go for a deal that extends tax cuts for incomes over $250,000. He thinks his win gave a mandate on that matter above all else, and exit polls showed most voters were with him. Boehner said the House would consider raising tax revenue by fixing the tax code and boosting the economy, but not through higher rates.
It is not clear how that standoff will get settled before year's end. And that's just the House.
Obama also still has to deal with Senate Minority Leader Mitch McConnell, R-Ky., whose disciplined band of Republicans just got more conservative with the addition of tea party-backed Republicans like Ted Cruz of Texas and Jeff Flake of Arizona. McConnell is up for re-election two years from now in a state that produced tea party favorite, Sen. Rand Paul, who McConnell opposed in the 2010 Kentucky GOP primary.
The president's approach, meanwhile, is heavily influenced by the debt debacle in the summer of 2011. Viewing that as a period of outreach that backfired on him, Obama goes into fiscal negotiations now with no incentive to give ground on what the White House calls tax cuts for millionaires.
"That's not bipartisanship. That's not change. That's surrender," Obama warned in the final days of the campaign. "That's surrender to the same status quo."
Obama's thinking, too, is that Republicans will have to help him fix the nation's broken immigration system or risk alienating a Hispanic population that could torpedo the GOP's electoral power for years.
Voters created this dynamic because they themselves are increasingly polarized. The nation was split 50-48 percent in choosing Obama over Romney. The share of moderate voters in the middle keeps shrinking.
There are signs of hope for compromise.
Karen Fitzgerald of Miami was all but grieving Republican Mitt Romney's loss to Obama. Throughout the election, her friends, most of whom are Democrats, had chided the Republicans on Facebook. On Wednesday, she saw a different theme in their posts.
"Now they're all saying we need to work together and be united," she said. "Maybe we can."
Associated Press writers Christine Armario in Miami and Ken Thomas and Andrew Taylor in Washington, and AP Polling Director Jennifer Agiesta contributed to this report.
AP White House Correspondent Ben Feller has covered the presidencies of Barack Obama and George W. Bush. Follow Feller on Twitter at www.twitter.com/BenFellerDC