I suspect that a court would find infringement rather than fair use here. This differs from the spat of election year "I'm a liberal/conservative musician and I don't want the conservative/liberal candidate to use my music" because the music cases are covered by public performance rights. Here, Christie has taken a significant segment of copyrighted material and used it to comment on his opponent. this would appear to exceed what is usually permitted by parody. But this is not a parody fair use case. It is a political speech case, which is somewhat different.
I also thought the ad was pretty funny.