Ok, so I'm probably making more of this than I need to ...

I am replacing outlets to match new paint in a room and did not notice
that one electrical box still has the old screw in the bottom hole ...
evidently it broke in the hole. There is nowhere to grip it on either
side, not even with needlenose pliers. The plies basically slide off
as soon as I go to turn it.

Can I take a tiny drill bit and drill it out or is there an easier
way?