Rudy Giuliani would be a bad choice as running mate for John Sidney McCain III for a variety of reasons.
Geography. The Northeast is out of reach to the GOP, so picking a Northeasterner is a complete waste. Moreover, New Yorkers, who are most familiar with Rudy, hate him. Rudy is most appealing to folks who don't know anything about him, and campaigning would blow that.
Ideology. McCain already has the secular fascist vote locked up, so Rudy isn't going to help him there. As for the Christianist base of the GOP, Rudy might be objectionable to them because of his utter lack of any of the virtues that they cherish. If anything, Rudy might inspire even more Christianists just to stay home on Election Day.
Baldness. I don't see how having two bald men can help.
Douchebaggery. Both candidates on the ticket should not be unmitigated douchebags.
Whom then should JSMcC select? Let's look at some of the same factors.
Geography. Forget the South. That's already wrapped up for the GOP, so a Southron running mate would be a waste. J Sidney has the Interior West covered. If he's looking for a geographical edge, he's going to have to get a Midwesterner. On the other hand, he could go for someone nationally recognized.
Ideology. The candidate should be a Christianist nutbag to shore up support in the base.
Baldness. The candidate should have a lustrous head of hair.
Douchebaggery. The candidate should have some charm and charisma, although J Sidney is probably stuck with a fellow douchebag given the other criteria. A flaming asshole might balance things out.
Based on the above criteria, I propose the selection of Alan Keyes. As Veep candidate, he wouldn't have to go up against Obama who made him look like an idiot in their Senate race. Christianists love him, and he's got recent African ancestry to give the GOP cover against charges of racism. He still has quite a bit of hair. He is such an incredible douche that his douchebaggery might actually make J Sidney seem likeable in comparison. He could turn douchebaggery into a strength for the ticket just as Dick Cheney's unprecedented assholery made GW Bush seem almost charming at times.
In the alternative, I propose Mel Gibson. Gibson has national name recognition and has played a lot of manly and heroic characters in movies, something that dumbasses, who are a key to this election for the GOP, often confuse with the candidate's actual background. He's as nutty as a fruitcake when it comes to religion, and his Passion of the Christ made him beloved among Christianists. He's got hair. Unless he's in a drunken rage, he doesn't come off as a douchebag at all. He can be a charmer. He may be acting for all I know, but he has the ability to counteract J Sidney's horrible personality.
But, you say, he's an anti-Semite, isn't he? Only when he's drunk, and he apologized for that incident. Besides nobody's more anti-Semitic than the Christianist Right who view Israel as the means to the long desired and awaited destruction of the Jews (except for 144,000 lucky converts to Christianity) that accompanies the Apocalypse. To them Israel is just a huge concentration camp, and the more of them that can be persuaded to move there, the better. The Israelis know this but court their support anyway, and staunch support of Israel trumps charges of anti-Semitism every time.
Remember that you read it here first, that Alan Keyes or Mel Gibson will get the nod. If not, J Sidney's campaign is doomed.