OVER THE PAST two years, politicians and pundits held out the hope that the 2012 election would definitively resolve the grand struggle between irreconcilable visions of the nation’s two major political parties. As Rep. Paul Ryan (R-Wis.) put it in May, one side would gain the “moral authority” to impose “permanent” and “fundamental” ­reform.

This was always a partisan fantasy, as the results Tuesday made clear. Just about half of voters — 50.4 percent — supported President Obama. Just about half didn’t. Democrats kept control of the Senate, Republicans kept control of the House. The nation was starkly divided before, and it remains starkly divided today.

But perpetuating the status quo of power-sharing does not doom Washington to more gridlock and obstruction. On the contrary: Now that it is clear no mandate will sweep away the opposition, politicians could acknowledge that the only way to get anything they want is to let the other side have some things it wants.

This won’t be easy, and it shouldn’t be. Republicans and Democrats are motivated by conviction as well as the imperative of political survival. Many Republicans honestly believe that raising taxes will slow economic growth. Many Democrats genuinely think the way to safeguard Social Security is by raising taxes on the wealthy. Voters wouldn’t respect them much if they blithely tossed away those convictions, especially after they just promised during election campaigns to stand firm.

We happen to think that, on a lot of the big issues, the fundamentalist solutions are illusory. Taxes should be kept as low as possible, but as the population ages, the government is going to need more revenue. High earners should pay more or get less from Social Security, but its promise of ever-richer benefits for each succeeding generation also will have to be trimmed. However, even politicians who reject these arguments will have to adjust to a reality where compromise is essential — where if they insist on getting everything, no one will get anything.

There are practical reasons for at least a touch of optimism on this score. Mr. Obama will no longer be focused on reelection. Senate Minority Leader Mitch McConnell (R-Ky.), who set Mr. Obama’s defeat as his priority, was not rewarded with a move into the majority leader’s office. The most explicit opponent of compromise in this election cycle, Indiana Republican Senate candidate Richard Mourdock, went down to decisive and richly deserved defeat. A number of reelected and newly elected senators may be inclined, by temperament or purple-state pressure or both, toward compromise: Virginia’s Timothy M. Kaine (D), independent Angus King of Maine, Indiana victor Joe Donnelly (D), Tennessee’s Bob Corker (R), Heidi Heitkamp (D) of North Dakota. While Speaker John Boehner claimed Wednesday that the election provided no mandate for higher tax rates, he also called for a “bipartisan agreement” on the debt. It’s not in Republicans’ interest to be seen as obstructionists or to wage budget war for the next two years.

“In the coming weeks and months,” Mr. Obama said in his acceptance speech early Wednesday morning, “I am looking forward to reaching out and working with leaders of both parties to meet the challenges we can only solve together.”

Yes, we’ve heard it before. But today the congressman who hoped for the moral authority to impose “permanent” reform is a defeated vice-presidential candidate. No honest person on either side can justify delay or defend political purity on the grounds that a landslide, mandate election is just around the corner. They’re left with one option: what Mr. Obama called “the hard and frustrating, but necessary work of self-government.”