WASHINGTON—Lawrence Summers pulled out of the contest to succeed Ben Bernanke as chairman of the Federal Reserve after weeks of public excoriation, forcing President Barack Obama to move further down the list of contenders to head the central bank.

One leading candidate is Janet Yellen, the Fed's current vice chairwoman, who has garnered substantial support among Democrats in Congress and among economists. But the public lobbying on her behalf appears to have annoyed the president, say administration insiders, and may lead...