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Cooperation, they said, was the message of the elections.

But Republicans rejected that.

“Tuesday’s election was not about Republicans; it was about the Democrats. They got a report card. They got an F,” Mr. McConnell said in a speech to the Heritage Foundation.

He said voters Tuesday were not patting Republicans on the back for what they might do, but rather were rewarding them for what they already have stopped Mr. Obama from doing — the obstructions that earned them the label of the “Party of No” from Democrats.

“If we had not done this, the administration would never suffer the consequences for pushing policies Americans opposed,” Mr. McConnell argued, saying that by opposing Mr. Obama at every turn, the GOP was giving voters “a clear alternative.”

The Kentuckian was buoyed by the results of Tuesday’s elections.

Despite defending six open seats in the Senate, not a single Republican-held state was lost Tuesday. In the House, the GOP lost just three seats, all in heavily Democratic districts.

“The White House has a choice: They can change course, or they can double down on a vision of government that the American people have roundly rejected,” Mr. McConnell said. “If they choose the former, they’ll find a partner in Republicans. If they don’t, we will have more disagreements ahead.”

Mr. Obama this week already has moved, at least slightly, on two major issues.

He said he no longer believes he can pass a broad energy bill that would impose limits on greenhouse gas emissions, and instead called for all sides to work on renewable and clean energy sources, such as nuclear power.

The White House also signaled movement on tax cuts — the issue that deeply divided Congress just before it left town in September, and that will await lawmakers when they return this month.

Mr. Obama earlier said the Bush tax cuts that went to wealthier Americans must be allowed to lapse. But asked about a temporary extension, Mr. Gibbs said Thursday that Mr. Obama would “be open to having that discussion and open to listening to what the debate is on both sides of that.”

Still Mr. Gibbs said the extension couldn’t be open-ended.

“The president does not believe — and I think would not accept — permanently extending the upper-end tax cuts,” the spokesman said.

Other possible areas of cooperation listed by Mr. Gibbs include ratifying a nuclear arms reduction treaty, working on child nutrition and acting on the recommendations of the commission Mr. Obama established to suggest ways to reduce the deficit.