But it was unclear Friday whether the Treasury Department would stand behind any deal, particularly after the Bush administration took control of the nation’s two largest mortgage finance companies, Freddie Mac and Fannie Mae, only days ago. Treasury officials let it be known that, this time, they would not be putting any taxpayer money on the line.People with knowledge of the thinking of the Treasury secretary, Henry M. Paulson Jr., said Friday that he was opposed to providing taxpayer money to push through a deal that could save Lehman.

In any event, some sort of resolution is expected over the weekend. The test will come if potential buyers balk at a purchase without the Fed’s backing. If that were to happen, federal officials would be left to evaluate what risks a sudden collapse of Lehman might pose to the broader financial system.

The rapid decline of Lehman underscores that investors remain unnerved, with rumors about an institution’s problems quickly becoming a self-fulfilling prophecy, as other banks seek to distance themselves to limit their financial exposure.

At this point, Lehman has few options.

Its stock’s relentless decline has convinced Richard S. Fuld Jr., Lehman’s chief executive, that the time has come to let go.

Image Suitors of Lehman Brothers are seeking help from the Federal Reserve to help make an acquisition palatable. Credit... Michael Falco for The New York Times

“He’s shell-shocked, but he knows he has to sell,” said one person who recently spoke to Mr. Fuld.

Lehman, which employs nearly 25,000 people around the world, tried to convince investors on Wednesday that it could survive on its own by selling divisions and spinning off commercial real estate assets, but its stock continued to decline. Any buyer would almost certainly cut thousands of jobs as it absorbed Lehman’s operations, which include a valuable money management division.