Around here the drywall contractors charge by and get a buck to $1.10 per square foot of finished drywall on a turnkey job. I imagine you can find some guys to do it cheaper.
Most would rather do new construction and charge more on remodels. Most also only want to mud and tape their own drywall installations. It hasn't been that many years ago you could get someone to do the labor only for $.16 per sq.ft., then the housing boom hit and it went to $.24 in less than a year. It is more now. The cost of drywall is now about .25 to .30 per sq.ft. Mud has gone up also.