Wary of appearing presumptuous, the White House has avoided overt moves to prepare, but it already has long dossiers on a host of candidates after last year’s nomination of Sonia Sotomayor. If Justice Stevens retires, Democrats close to the White House said, the leading contenders will be three runners-up from last year: Elena Kagan, the solicitor general; Diane P. Wood, an appeals court judge in Chicago; and Merrick B. Garland, an appeals court judge in Washington.

The choice would depend in part on what kind of fight Mr. Obama is willing to wage amid other tough legislative battles. Energized if bruised from his campaign to overhaul the nation’s health system, Mr. Obama this year wants to push through energy, education and financial regulation measures, ratify an arms control treaty and make progress on immigration legislation.

A confirmation battle could not only provoke fresh skirmishing on longstanding issues like guns, abortion, race and terrorism; it might also generate new divisions stemming from constitutional challenges to Mr. Obama’s new health care program and a recent Supreme Court ruling guaranteeing the right of corporations and unions to spend unlimited amounts of money in candidate elections.