Dan Erlewine talks of just such a dilema in his Guitar Player Repair Guide. I will Paraphrase:
Get a small length of metal tubing, slightly larger than the O.D. of the broken screw, grind one end into teeth, chuck it into a drill, and it will drill AROUND the broken screw (not all the way through the headstock). Now, wiggle the wood and screw till it snaps off, and remove the broken screw/wood plug. Plug hole with appropriate dowel, enlarging made hole if necessary.
Hope this makes sense, and helps. In short, unless you can get the screw to back out, by grabbing it, there appears to be no easy fix.