This is a Left-Wing trap. Sure, Rudy Giuliani would be a very attractive candidate: he would draw in a lot of "moderates", and he could even help GWB squeak out a victory in New York. Granted, that's a long shot at best, but he could force the Democrats to spend so much more time and money defending New York that they will be unable to go after any of the "Red" states the President won in 2000 (and, in the process, offset the popular vote differential by which the Democrats claimed to have "won" in 2000).
The downside, the "trap" part, is that by "dumping" Dick Cheney the President will be tacitly agreeing with the Vice President's critics who have branded him a "corporate crook" and the "evil genius" behind the "failed and unnecessary" war in Iraq. Plus the DNC, with the assistance of the Moby's of the world, would remind Republicans and conservatives of Mr. Giuliani's presumed "social liberal" tendencies. Many on the Right could be inclined to stay home. In the end, win or lose, the Left would get at least part of what they want by "nailing" the evil Cheney. Besides, anyone who saw Dick Cheney systematically demolish Joe Lieberman in their debate will know that he is someone who could make a John Edwards or Hillary look like the rank amateurs they are (as opposed to a Rudy, who would probably end up agreeing with a "progressive" Democrat, as often as not).
"many on the right would be inclined to stay home" I hope not. It's true that conservatives are taken for granted from time to time just like blacks are by the rat party. But the truth is that neither constituency has anywhere to go. The chance of getting a newt gingrich/ronald regan type admistration anymore dwindles every year. We are lucky GW fought terrorism! It's a sick new gotcha politicla world out there. But what can you do?