REPUBLICANS COLLECTED a significant victory in Tuesday’s midterm elections, gaining control of the Senate to go with their control of the House. With that win comes an increased level of responsibility for the nation’s fortunes. They can no longer behave like a petty opposition party. If the GOP wants to prove before 2016 that it is better at governing than the Democrats, this is its chance to address a backlog of problems — to seek results, rather than continue to blame others for failure.

That is not the only possible path, of course. Ascendant Republicans could conclude that a strategy of rote anti-Obama opposition and ideological point-scoring put them on a path to power and should be maintained. For their part, Democrats might be tempted to discount Tuesday’s results as the inevitable consequence of a uniquely tough Senate map; they, too, might see little reason for give and take. President Obama could turn to unilateral executive decisions that take compromise off the table.

But those depressingly familiar strategies haven’t worked out well for the country, and they haven’t worked for the parties, both miserably unpopular, according to exit polls. Republicans captured battleground Senate seats and made close runs at some others. At the same time, they did not claim anything close to 60 seats, the magic number that would allow them to bypass Democrats, and of course the White House remains in Democratic hands. The country has empowered Republicans — to share power.

Republicans, then, should treat the next two years as an opportunity to legislate in good faith, not to push serious work beyond the next election in the fantasy that the country has permanently turned in a more conservative direction. For his part, Mr. Obama should not embark on his final two years with an assumption of Republican intransigence that would be self-fulfilling.

A full debate on the United States’ fight against the Islamic State is past due, with significant congressional review of and consent to the sustained air campaign over Iraq and Syria still lacking. The “sequester” — those utterly irrational, across-the-board budget cuts that should never have come into effect — is set to hit harder next year. Lawmakers have plenty of reasons to head off the budget sledgehammer, from preserving military readiness to maintaining investment in programs that sustain Americans’ quality of life. The country’s roads, rails, bridges and bus lanes have been starved of decent policymaking for years: Lawmakers have repeatedly ducked responsibility for providing sustainable funding for the infrastructure that keeps the nation moving. The policy isn’t difficult — the problem is Congress’s incapacity to make even obvious choices. The country’s immigration system remains wildly contrary to the national interest. And so on.

The next Congress is capable of addressing these matters, and more, in concert with Mr. Obama — if GOP leaders choose to channel their party’s enthusiasm into tangible results rather than just drawing lines in the sand, and if the president leads more deftly than he has in the past. Voters expect, and have a right to expect, something better than what Washington has delivered over the past two years.