But Mr. Geithner has not yet notified the White House of his intentions, and family considerations could still win out, advisers say.
Speculation from Washington to Wall Street has intensified because Mr. Geithner, the only holdover at the center of Mr. Obama’s original economic circle, said a month ago that he would decide on his future after the White House and Congress reached a deal to increase the nation’s debt ceiling. Mr. Obama signed that deal into law on Tuesday.
Mr. Obama and his chief of staff, William M. Daley, have been urging Mr. Geithner to stay, administration officials say, not only for continuity when the economy has weakened and to avoid an all-but-certain confirmation fight in the Senate over a successor, but also because Mr. Obama has developed a close rapport with Mr. Geithner.
Whether the president persuades Mr. Geithner to stay will be a central development for the White House as it girds for a re-election race expected to turn on the economy and the continuing battle of the budget with Republicans.
Mr. Geithner has been considering an exit since early this year, administration officials say. None would speak directly on what Mr. Obama has said to his Treasury secretary because the two men have private meetings alone once a week.
On Monday, after the previous night’s announcement of the debt accord, Mr. Geithner convened advisers to talk about his future agenda, including dealing with the European debt crisis, housing and overhauling the corporate tax code. Aides say they took that as a clue he was staying, only to wonder on Tuesday, when a photographer came in to capture Mr. Geithner watching the final vote for the debt deal, if the photos were intended as a record of Mr. Geithner’s final days.
Especially in recent weeks, the issue has become a running joke, officials say: Mr. Geithner and Mr. Daley tease about the ankle bracelet that the White House makes him wear, or Mr. Geithner asks if Mr. Daley has yet read his resignation letter, to which Mr. Daley answers in unprintable language.
But the pressure from the top on Mr. Geithner was more serious one day about two weeks ago, officials say. Mr. Daley has also told Mr. Geithner’s top lieutenants — Deputy Secretary Neal S. Wolin and Mark A. Patterson, the chief of staff — that he wants them to remain, though Jake Siewert, Mr. Geithner’s counselor, is returning to New York as soon as this week.
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.”
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