GW Bush sings (in a Rex Harrison sort of a way) The End of the World As We Know It.
This one might actually make your head explode.
So do we have a new art form here — mashing up samples to make unlikely/impossible singer/song combos? If so, it's a temporary thing. Part of the fun is that some of the rivets show. When the technology gets so good that it becomes child's play to make Hillary Clinton do a duet with Dick Cheney on “I Got You Babe,” then it won't be fun any more.
Obligatory link to Sonny & Cher (1965) and much more interesting link to two of the less likely people ever singing “I've Got You Babe” (1973).