If confirmed by the Senate, Mr. Lew, 57, would be Mr. Obama’s second Treasury secretary, replacing Timothy F. Geithner, the last remaining principal on Mr. Obama’s original economic team, at the head of that team.

While Mr. Lew has much less experience than Mr. Geithner in international economics and financial markets, he would come to the job with far more expertise in fiscal policy and in dealing with Congress than Mr. Geithner did when he became secretary at the start of Mr. Obama’s term. That shift in skills reflects the changed demands of the times, as emphasis has shifted from the global recession and financial crisis of the president’s first years to the continuing budget fights with Republicans in Congress to stabilize the growth of federal debt.

The partisan tension over the budget between Mr. Obama and Republicans suggests that Mr. Lew will face a grilling by Senate Republicans in confirmation hearings. But despite weeks of speculation that Mr. Lew would be named Treasury secretary, Republicans have not signaled that they plan to mount the kind of opposition they raised to Mr. Obama’s potential nomination of Susan E. Rice, the ambassador to the United Nations, for secretary of state, and Chuck Hagel as secretary of defense; the president named Mr. Hagel on Monday, and eventually settled on Senator John F. Kerry, Democrat of Massachusetts, for secretary of state.

Mr. Lew’s departure would create an important vacancy for what would be Mr. Obama’s fifth White House chief of staff, a turnover rate that is in contrast with the stability at Mr. Geithner’s Treasury. Leading candidates are said to include Denis McDonough, currently the deputy national security adviser in the White House; and Ron Klain, a former chief of staff to Vice President Joseph R. Biden Jr.

Mr. Lew had a brief turn in the financial industry before joining the Obama administration four years ago, working at the financial giant Citicorp, first as managing director of Citi Global Wealth Management and then as chief operating officer of Citigroup Alternative Investments.

His first job with Mr. Obama was at the State Department, where Mr. Lew was the deputy secretary responsible for managing day-to-day operations of the department and its international economic policy. Secretary of State Hillary Rodham Clinton protested to Mr. Obama when the president in 2010 tapped Mr. Lew to replace Peter R. Orszag as budget director.

It was Mr. Lew’s second stint heading the Office of Management and Budget. He previously served in President Bill Clinton’s second term, helping to negotiate a bipartisan budget deal with Congressional Republicans that led to four years of budget surpluses. In the 1980s, Mr. Lew was a senior aide to House Speaker Thomas P. O’Neill, a Democrat, also advising in budget negotiations with President Ronald Reagan.

He has been deeply involved in the deficit negotiations over the last two years. And, if he were quickly confirmed, as Treasury secretary his first test could come as soon as next month, when analysts expect a fight over raising the debt ceiling, which is the legal limit on the amount that the government can borrow.

Republican leaders have said they would refuse to raise the ceiling unless Mr. Obama agrees to equal spending cuts, particularly in entitlement programs like Medicare and Social Security. Mr. Obama has said that he will not negotiate over the ceiling, with the country’s full faith and credit at stake.

With battle lines already drawn, the country is expected to run out of room under the ceiling sometime between mid-February and March. At that point, Congress would need to raise the borrowing limit, or the country would start defaulting on obligated payments, like those promised to seniors, doctors, contractors and bondholders.

Mr. Lew’s role as an Obama negotiator in 2011 did not endear him to Republicans, in particular House Speaker John A. Boehner, and he took a lower-profile role in the most recent negotiations at year-end. The White House was eager to avoid controversy given the likelihood of Mr. Lew’s nomination to Treasury. Instead Mr. Geithner and Rob Nabors, the director of legislative affairs, were lead negotiators.

Mr. Lew, a native of New York, is known for his low-key, professorial style and organizational skills. While he was a favorite of Mr. Obama and other staff members as chief of staff, Mr. Lew made it known that he did not want to continue in that post for a second term.