Know what's ironic? Rudy Giuliani needs Hillary Clinton. She defines him. She is, perhaps, the reason to elect him.
As such, she is not his archenemy, but his nemesis ...
If you're unfamiliar with the nemesis/archenemy distinction, Chuck Klosterman explained it as good as anyone ever has, back in '04. Here's the difference between the two:
...You kind of like your nemesis, despite the fact that you despise him. If your nemesis invited you out for cocktails, you would accept the offer. If he died, you would attend his funeral and—privately—you might shed a tear over his passing. But you would never have drinks with your archenemy, unless you were attempting to spike his gin with hemlock. If you were to perish, your archenemy would dance on your grave, and then he'd burn down your house and molest your children. You hate your archenemy so much that you try to keep your hatred secret, because you don't want your archenemy to have the satisfaction of being hated.
The truth is that every great person, team, etc. needs a nemesis to achieve their full potential.
Would Muhammad Ali have been as great without Joe Frazier? No way! Would the Red Sox be interesting without the Yankees? Not to me.
Heck, this phenomenon even works in cartoons. Without Lex Luthor, Superman is just a dude wearing panty hose. ... Batman without the Joker? Puh lease!
To win the nomination, Rudy needs Hillary like the Redskins need the Cowboys. Ok, way more ...