With Mr. Obama back at the White House on Tuesday after a holiday vacation in Hawaii, White House aides said some personnel decisions could be announced perhaps this week. Among the announcements expected soon is a successor to Lawrence H. Summers, who has returned to teach at Harvard, as the chief White House economic adviser.

The leading candidate is believed to be Gene Sperling, who held the job under President Bill Clinton and is currently a counselor to the Treasury secretary, Timothy F. Geithner. Other candidates have included Roger C. Altman, a Wall Street financier who was a deputy Treasury secretary under Mr. Clinton, and Richard C. Levin, an economist and the longtime president of Yale University.

Ron Klain, Mr. Biden’s chief of staff for the past two years, told colleagues on Tuesday that he was leaving at the end of January. He will become president of Case Holdings, the parent company of the investment firm started by a previous boss, Steve Case, the former AOL chairman.