We never did get the bit out of the drill. So I went to Lowes and bought another cordless drill. I have to say, it is tiny!
Which suits me fine. It will be so much easier to haul around the woods than the old one. Although the 5/16th bit looks a bit silly in it. I spent a bit more than I wanted getting the $50 drill verses the $20-$30 model. However, this was the cheapest one with a replaceable battery so I hope to get a long lifespan out of her.