I would say he would probably vote conservative, but I doubt he'd be part of either party.
I don't see any way he'd be a Dem, though... He was too much for personal accountability.
Let's see: Promotes personal responsibility, deep personal faith, ultimate truth, defines adultery as including the lusts of the heart (no quibbling over the definition of "is"), taking care of the poor ourselves instead of having the government do it, protecting the children (including those in the womb) . . . yeah, right, He was a Democrat. *BIG rolleyes*
Ultimately, though, Jesus was a monarchist rather than a Republican--with Himself as the Monarch.