How deep does the bite have to be before you would get rabies?

Not deep at all: A minor scratch can transmit the virus.

Rabies: Rabies is a preventable viral disease of mammals most often transmitted through the bite of a rabid animal. The vast majority of rabies cases reported to the Centers for Disease Control and Prevention (CDC) each year occur in wild animals like raccoons, skunks, bats, and foxes. http://www.cdc.gov/rabies/index.html