That's well and good and makes sense as far as it goes. But what, precisely, is there for them to compromise on? Or will Republicans just pass a lot of bills that Obama vetoes?
Let's start with incoming Senate Majority Leader Mitch McConnell's first priority: voting to approve the Keystone XL pipeline. Obama continues to insist that he will make a decision only once he's sure that the pipeline won't seriously increase carbon emissions, and lately the administration has seemed to hint it's leaning against the project. But there's speculation that Obama might cut a deal, trading approval of Keystone to keep new EPA carbon-emissions regulations in place. Another possible area of agreement is free-trade deals—if McConnell and Obama can overcome populist elements in their own parties, the Tea Party and a newly invigorated, Elizabeth Warren-led band of Democrats.
There will be plenty to fight over, though. Some time in 2015, Congress will need to raise the debt ceiling. Loretta Lynch, the president's nominee for attorney general, and Ash Carter, his nominee to lead the Pentagon, both still await confirmation. Both should be confirmed, but there could be interesting battles in the process. Republicans will continue to search for ways to stop Obama's executive actions on immigration. Although party leaders now seem resigned to Obamacare's existence (at least as long as Obama is in office), there will probably be continued symbolic efforts to repeal it, if nothing else to appease conservative elements on the Hill and in the electorate. And as Ted Cruz's failed maneuver earlier this month showed, he's still liable to throw Congress into chaos now and then, with unpredictable results.
So the real action will come in three theaters: statehouses, courts, and the presidential campaign. Why state capitals? Because unlike Washington, they're not frozen by the same kind of polarized division. Single-party dominance in the states was already at a recent peak before November, and now it's more extreme. Consider this: Republicans control 68 of 98 state legislative chambers. In 23 states, they control the entire legislature and the governorship. Even after their debacle, Democrats can claim complete control of another seven states. The reasons for this sorting are complex and hotly debated; the important part for our purposes is it means it's much easier for a party to get its way at the state level. As Politico notes, the No. 1 action item is likely to be tighter restrictions on abortion.
While Obamacare is probably safe from Congress for now, it could be in deep trouble at the Supreme Court, where justices will hear arguments in King v. Burwell. While liberals deride the case as nothing more than a fight over a typo, the Court could easily kill off federal health-insurance exchanges. Meanwhile, the nation is likely to see the continued expansion of marriage equality, as more and more courts strike down laws banning same-sex unions.