Soren Dayton takes a look at early polling data from Pollster.com, comparing a Clinton-Giuliani race to a Clinton-Bloomberg-Giuliani race. Either way, the news right now is bad for the GOP:

1. Even without Bloomberg, Giuliani loses nearly every swing state. Giuliani would win only Missouri and Washington. Note that WV, CO, NV, AZ, PA, MI, and FL are not included in this sample. 2. Bloomberg seems to take his votes from both sides, but somewhat more from the GOP. However, in the swing states, the damage seems to be almost 2-1 against the GOP. However, these results are almost all within the margin of error.

I'm personally not big on horse race reporting, and these are way early polls anyway. But at least it gives you some idea where Bloomberg's support might come from.