I think Republicans (and everyone in Washington really) drastically over-estimate how unpopular raising the debt ceiling is. Sure, hardcore teapartiers will base their vote on it, but otherwise it's not a huge game changer. I seriously doubt most Americans even understand what it is.
It's not even a minor game changer, people simply don't care all that much about the debt. Even with the huge amounts of media attention on the debt, 42% of Americans think the government should be focused on reducing unemployment as opposed to decreasing the debt.
The idea of Republicans running ads against Democrats for voting to increase the debt ceiling makes me lol. All it takes is one counter ad describing what would happen if the debt ceiling wasn't raised and any small advantage gained by McConnell electorally is dashed.