Nathan, I wouldn't pull the carb off. If it was me, I would tape around the little boss area that the bolt is broken off in, and then put masking paper completely over the carb so that only the boss is peeking through the paper and it is totally taped off. Then I'd use an Easy-Out tool while I held the hose from the shop vac on it as well. Normally I would heat it up with a flame as well, but not on the carb.
We don't need you blowing your car up.