But there was another level, and it practically screamed, “Hey, don’t rule me out in 2008.” His constant travels — the schedule this weekend puts him in California and Texas, two states dripping with electoral votes — can only feed assumptions that he is toying with a third-party candidacy.

He wasted little time on Thursday to slip in the buzzword of the year: change. All the presidential candidates say they want to be change agents so badly that the eventual losers might think about looking for work in a movie theater box office.

“People might be saying, ‘C’mon, do your job,'” said Maurice Carroll, director of the polling institute at Quinnipiac. “Maybe people are thinking, ‘Look, it’s such a long shot; why don’t you think about what to do about traffic congestion in Bay Ridge?'”

Others offered a blunter assessment.

“It’s a very long prelude, and I think it is becoming a very old story very fast,” said Robert Zimmerman, a communications specialist who is one of Senator Hillary Rodham Clinton’s fund-raisers. “Mike Bloomberg has failed to make a case that he represents an independent movement, as opposed to a former Democratic liberal, former Republican, former Bush-backer running a campaign of opportunism.”

To be sure, there is little indication that ordinary voters around the country have given much thought to a Bloomberg candidacy, especially given the dramatic primary races in the two major parties. But his enormous wealth and willingness to spend it make him someone who cannot be ignored within the political world.

At this point, the fatigue with Mr. Bloomberg’s national ambitions seems highest within the political chattering class, but it could spread if the mayor continues to dance around his intentions without saying clearly what they are, analysts said. The speculation began in earnest last June, when he switched his registration from Republican to independent.

Health inspectors, armed with handheld computers, have begun combing blocks in The Bronx to catalog signs of rat life and conditions that make them thrive.

After the “rodent indexing” of a particular neighborhood, officials would bombard the area with repeated exterminations.

After gaining national media attention for spearheading an almost total ban on trans fats in city restaurants, Bloomberg was photographed in this month’s issue of Wired magazine munching on those very same dangerous fats.

The photo, which accompanies a short Q&A about technology and politics, features Bloomberg at his City Hall desk, looking thoughtful and serious. Meanwhile, his right hand seems almost absent-mindedly pulling a Cheez-It out of a single-serving bag of the crackers.

The reader can only assume that the baked snack cracker is headed for the mayor’s mouth, and along with it some of the half-gram of trans fat found in every serving of Cheez-Its.

. . .