I recall talking about this a while back with a couple of guys, both of them young, conservative-leaning academics disillusioned with Bushism.  One, a McCain backer, absolutely would not touch Giuliani because "he's a fascist."  The other, a Giuliani backer, was fearful of McCain's "finger on the button."

So aside from the fact that these two guys were both right, McCain's temper is a widely held concern.

Of course you could always just ask Senator Cochran.