To supporters of other campaigns, this branch of the Bloomberg operation appears to have another effect. By pursuing contributors and asking them to get involved in his candidacy — without actually donating money to him — Mr. Bloomberg could have the effect of dampening fund-raising for opponents who cannot underwrite their campaigns with personal wealth…

The approach comes straight out of Mr. Bloomberg’s re-election playbook of 2005, when his team locked down the biggest Democratic donors in New York City by bringing them onto his mayoral campaign as blue-chip endorsers. As he is doing now, he was financing his own campaign. But their support helped wipe some of the most important Democratic financiers from the contributors’ list of his donations-dependent Democratic challenger, Fernando Ferrer.

They also gave Mr. Bloomberg, then a Republican in an overwhelmingly Democratic city, the imprimatur of an important segment of the Democratic establishment, which his aides hoped would serve as a permission slip for any rank-and-file Democrats wary of pulling the Republican lever for Mr. Bloomberg.