Hmmm....well....if it's the only screw holding it down, is it possible to rotate the wood to unscrew it from the screw threads?
If not, you could sink a hole on either side of the remainder of the screw as close as you can get and then the wood should come loose, leaving the screw. Then just stick a pair of vice grips on it and twist it out. You'd have a larger hole for the screw than was there before, but it would be out.
In the future....
Whenever I have this happen, rather than trying to drill it out (which rarely works as you found out) I use a cutting wheel on my drill that cuts a groove in the head of the screw, then use a large flat-head to twist it out. Works every time.