OP:
I think this is your problem - the drain plug looks like one of those broad shouldered ones that has a o-ring underneath the shoulder of the bolt head. It's been my experience that these plugs can be very difficult to remove, even when they are torqued to spec.
WARNING - whatever you do, make sure you have the 3/8' socket/extension head inserted ALL THE WAY INTO the recess. I strongly suggest that you get the vehicle up high enough so that you can apply adequate and proper leverage. I agree with the previous poster who suggested 24 inch breaker bar. Do NOT use an impact driver!
And be prepared, when that plug loosens it will do so instantly. Don't smash you knuckles! And be careful you don't push the car off the jack stands!!!!!!!!!!!!!!!!!
If the plug is a flat shouldered one like I think it is, when you re-tighten in, go easy. About 10 or 12 lb/ft MAX.
Good luck, be patient, don't strip the recess, and be safe.
Scott