Charlie Cook is one of the more respected and listened to election analysts in DC. He thinks that it would take a lot for Bloomberg to win the Presidency:
Obviously, trying to win the presidency is an even more formidable exercise for an independent than for a major party nominee. An independent might start with the support of about 11 percent of the electorate. Combining that with the $1 billion that Bloomberg could pump into his own campaign, it might not be implausible for his support levels to hit the mid-to-high 20s, perhaps even attracting the 30 percent or so who seem particularly open to an independent candidacy. But for Bloomberg to get from, say, 30 percent to the high 30s, the level probably needed to win the necessary 270 electoral votes, the public would have to be repulsed by both major parties' nominees because they had been so badly damaged.
Right now it seems there's a good chance that both parties' bases will be largely satisfied with their nominees. Certainly Hillary seems to have pacified the extreme Left wing of her party pretty well -- with guys like Markos Moulitsas saying nice things about her, there probably won't be much room to her Left. And if Fred Thompson or Mitt Romney is the GOP nominee, he probably begins with the base locked up. With regard to Rudy Giuliani however, it's hard to see how Mike Bloomberg would have room to steal his base.
So will Bloomberg try to beat the odds?