Schwarzenegger did the same thing. His strategy was that he didn't need the folks on the right as he would capture the great middle.
I kept asking the ArnoldBots what the political platform of the great middle was (a little bit of socialism? an average amount of property rights? etc). I never got an answer. Go figure! ;-)
I guess Guiliani (like Arnie being forced to cut Cali services) is learning the hard way----too bad (/sarc).