Other Democrats heaped criticism on the Republicans. Senator Elizabeth Warren of Massachusetts said on Twitter: “Abandoning their Senate duties would also prove that all the Republican talk about loving the Constitution is just that — empty talk.”

Activists and interest groups quickly engaged in the Senate fight. “I have never heard from so many organizations in D.C. and outside who are worried and concerned and want to participate in a campaign,” said Nan Aron, the president of the left-leaning Alliance for Justice. “This is totally different from anything that has happened the past few years. The energy and fear is palpable.”

In choosing a nominee, Mr. Obama could pick a liberal version of Justice Scalia, which would fire up Democrats but would virtually ensure that Republicans would block the nomination in the Senate. Or he could choose a moderate — someone who built a career as a prosecutor or a corporate litigator, with little record on culture-war issues — which could increase pressure on Republicans to allow a vote.

But that could pose other problems. If Mr. Obama passes up the opportunity to put forward a liberal in favor of someone who represented corporations, it could provoke sharp criticism from the left. The danger is not just reducing potential voter enthusiasm from Democrats but roiling the Democratic presidential primary.

It was not yet clear which way the president was leaning. But some former White House officials said they would advocate a nominee with a proven record of support in Congress as a way of making it more difficult for Republicans to oppose the nomination.