Neither Mr. Geithner nor Mr. Daley would comment. “I haven’t made that decision yet,” Mr. Geithner said Tuesday in an interview with ABC. He added, “We’ve got a lot of challenges, president’s got a lot of challenges, and, you know, I got other pressures on me, too.”

Chief among those pressures are his family. Mr. Geithner’s wife and son moved back to New York in June so his son could complete high school there. And Mr. Geithner has been working at a breakneck pace since the early days of the financial crisis in 2007. Formerly president of the Federal Reserve Bank of New York, he has been among the three top stewards of the economy, along with Ben S. Bernanke, the Federal Reserve chairman, and the Bush administration Treasury secretary, Henry M. Paulson.

“He’s had a tough job during a tough time, and I think he’s really slogged through and made some really tough choices,” said Senator Mark Warner, Democrat of Virginia. “I can understand why he might want to cash it in.”

But, he added, “My fear is not only who would you get that would have the experience to grapple with another crisis but also, do we really need a massive confirmation fight?”

From the start, Mr. Geithner’s biggest critics have been on the left. But Jared Bernstein, a former member of the administration’s economic team and a liberal economist close to some of the critics, said: “To the extent people vilify Tim as only caring about banks, they’re way off. He’s always understood that Main Street depends on credit from Wall Street, and I know for a fact that he advocated the steps we took for that reason, not to preserve anyone’s capital or profits. I’ve actually heard him say some pretty nasty stuff about those guys.”

The prospects of being drawn into an election-year confirmation brawl could deter some who might be considered as Mr. Geithner’s successor. Among those named by people familiar with administration thinking are Jamie Dimon, the chief executive of JPMorgan Chase; Jeffrey R. Immelt, the chairman of General Electric and of Mr. Obama’s Council on Jobs and Competitiveness; Roger Altman, a deputy Treasury secretary in the Clinton administration; and Erskine Bowles, a former White House chief of staff to President Bill Clinton and co-chairman of Mr. Obama’s fiscal commission in 2010.

Some Democrats say Mr. Bowles might be one of the few people who could surmount the opposition of Senate Republicans, given his good relations with some of them after his work on the bipartisan fiscal commission. “In rational times, absolutely” Mr. Bowles would be confirmed, Mr. Warner said. “But I’m not sure we’re in rational times.”