Along the way, Mr. Summers has forcefully debated the Treasury secretary, his onetime protégé Timothy F. Geithner, over what to do with troubled banks. He has clashed with Peter R. Orszag, the budget director, over fiscal and health policy issues. He has collided with Austan Goolsbee, an economist on the Council of Economic Advisers, over whether to rescue Chrysler. And he and Mrs. Romer have squabbled over how best to make the economic case for overhauling health care…

Some advisers complained that, under Mr. Summers, meetings became “endless debating sessions,” a phrase used separately by two aides who asked not to be named given the delicacy of internal matters. As Mr. Summers sees it, his penchant for debate — he was a standout member of the debate team at the Massachusetts Institute of Technology — fits the job…

Mutual acquaintances say that the longtime friendship between Mr. Summers and the 47-year-old Mr. Geithner has been strained, but that their relationship would be even worse were it not for Mr. Geithner’s even temperament and his history with Mr. Summers. “I am completely comfortable pushing back at him,” Mr. Geithner said in an interview.