Beside the fact this would never, ever happens... even with his job approval around 30, Obama would beat Paul, as he's not going to win any election outside his congressional district. Period
I love the delusions Obamaniacs here have about how invincible their candidate and party are at this point.
We do in no way believe he is invincible. However the GOP would need to present a good candidate for Obama to be defeated, and not one of the schmucks that currently are front-runners. You can't kill a dragon when all you have is broken arrows and dull dagers. You need a sword. Paul ein't no sword.