Make sure your e-brake is not on. That will tighten the grip the shoes have on the drum and make it next to impossible to remove. Assuming that wasn't the problem...
A lot of brake drums have threaded holes on the face near the lugs. These holes are there to put in jacking screws for drum removal. Find one or two screws that fit the threaded holes and use them to push the drum off.
If there's no such holes, well, get a deadblow hammer and start banging. Penetrating oil from your local auto parts store will also help.