Some Democrats do not rule out the possibility that Mr. Obama and Mrs. Clinton could be playing it supercool, only to increase the splash of seeing Mr. Obama, the junior senator from Illinois, reach out to his old bête noire, Mrs. Clinton, the junior senator from New York, to become the first black man and the first woman to seek the White House as nominees.

“If he determines that Hillary after all is the best choice to help him to win and to govern,” said Dan Gerstein, a Democratic consultant in New York, “they are capable of pulling off what would be the greatest head fake in American political history.”