That's the subject of a disagreement between Jonathan Chait, who says they will if they retake the House, and Jonah Goldberg, who disagrees so strongly that he wants to bet $500 on the matter. Chait wants different stakes:
If Obama wins a second term, and a GOP-controlled House has not impeached him by 2017, I will let Goldberg write an item on my blog explaining why I was wrong. I'd hope he'll let me do the same on his blog if I'm right. Oh, I also predict that said impeachment will be endorsed by Goldberg.
Hold your gold. It's on now.