WASHINGTON — Mayor Bloomberg’s presidential flirtation — a topic once largely consigned to the pages of the New York City press — has gone national, igniting a debate over whether he will jump into the race and what impact his candidacy would have on the election.

A spokesman for Unity08, an online group pushing to draft a bipartisan presidential ticket, said Mr. Bloomberg was the type of candidate the organization was looking for. “It’s not for me or anybody else to anoint a candidate, but certainly Bloomberg is a very likely one,” the spokesman, “Law & Order” star Sam Waterston, said yesterday on CBS News’s “Face the Nation.”

The group will hold an online convention to pick a candidate, Mr. Waterston said, and the mayor has been frequently mentioned as a possibility. “He’s a very competent, very able, very successful mayor, and he’s chosen to be an independent,” he said of Mr. Bloomberg.

In the days since the mayor’s announcement that he was leaving the Republican Party sent the presidential speculation into a fever pitch, he has repeated his longstanding denials of a candidacy, but he has refused to rule it out.

“I personally believe he will be running,” Mayor Koch said yesterday on CBS. He said that even though he has endorsed Senator Clinton in the Democratic primary, he is not committed to a candidate in the general election and could support Mr. Bloomberg.

Both Mr. Koch and a former adviser to Ross Perot, Edward Rollins, said Mr. Bloomberg was in a better position to get on the ballot in all 50 states and run a credible campaign than Mr. Perot, particularly considering his wealth. Aides to Mr. Bloomberg have said he would be willing to spend as much as $1 billion in a presidential campaign.

Even if he doesn’t win, he could dramatically alter the race and exert great influence on the agenda of the victor, Mr. Rollins said. “At the end of the day, it may not be enough to draw voters to him to give him 270 electoral votes, but he certainly can set an agenda for this country, for the future, and for the campaign,” he said.

Talk of a Bloomberg candidacy has spiked as the mayor has increased his travel to large states awash with electoral votes, including California and Texas. He has been speaking out on national issues such as gun control and immigration since he began his second terms, but in recent weeks, he has escalated his disparagement of Washington inaction, warning last week that the country was “really in trouble.”

While he has criticized the slate of presidential candidates generally, Mr. Bloomberg has yet to speak out directly against his two most prominent potential rivals: Mayor Giuliani and Senator Clinton.