"My governor is a Jewish carpenter."
Now, leaving aside the pervasive fanaticism and, frankly, slavish fanboyishness in this sentence (it's like having a bumper sticker that says "I voted for President Superman"), it kills the joke. Because, see, the original gag -- "My boss is a Jewish carpenter" -- is actually kinda funny. You see it, and assuming you haven't heard it before, you think, oh, huh, this guy is open-minded, his boss is a WAIT HOLD UP HAHA I SEE WHAT YOU DID THERE, JESUS. It's not Groucho Marx, but it's moderately clever by the standards of Christian bumper sticker slogans.
But changing this up -- look, a person's boss could be anybody. But everyone knows who the governor is, and you look at this, and you have a totally different reaction: "Wait, did a Jewish carpenter run against Rick Perry? I...what?" IT MAKES NO SENSE AND IT KILLS THE JOKE.
Just so you don't think I'm just picking on the Jesus-jumpers here (although they make it hard not to), I parked next to a car today that had a bumper sticker reading "DOING MY PART TO PISS OFF THE CHRISTIAN RIGHT". Which is an admirable goal, I suppose, if you've got nothing better to do, but how does driving a nondescript white Honda piss off the Christian Right?