WASHINGTON  When Rahm Emanuel was running for Congress on the North Side of Chicago, he would often make calls while he was out shaking hands near the city’s elevated trains, with their distinctive rumbling sending an unmistakable signal that he was standing in his district.

Mr. Emanuel was born and raised in Chicago, but he has never been seen as one of the city’s towering figures. And that, his friends say, is one reason why being mayor of Chicago has long been among his biggest political ambitions.

But is it better than being chief of staff to the first president from Chicago?

To those who know Mr. Emanuel well, the answer is unquestionably yes, which is why they believe he is seriously weighing leaving the White House in the wake of Mayor Richard M. Daley’s abrupt announcement on Tuesday that he intends to step down next year.

“Something like that doesn’t come around a lot,” said Robert Gibbs, the White House press secretary, doing little to douse speculation about Mr. Emanuel. “It’s no surprise that’s a job he’s been interested in.”