So, who would be a strong pick? Some V.P. candidates fit one theory of the campaign, others another. And there seem to be at least four competing theories in the McCain camp, which, while not entirely mutually exclusive, point in different vice-presidential directions.

Given the political strength Senator Clinton exhibited as she dueled with Senator Obama to the end of the primary season, it is conceivable that Mr. Obama would turn to her. But his associates describe that as unlikely, saying that for a variety of reasons, Mr. Obama is not looking to have her as a running mate or serving with him in the White House.