If you can get a driver to bite at all, soak it in penetrating oil first for several hours. Just let it pool up in there and hope it creeps down into the threads. Maybe try getting some penetrating oil down from the other side too. Make sure its a good oil, like Kroil or acetone/ATF mixture. Don't bother with WD-40.
If you still can't get it out, a small extractor set might get do the job. You just need to make sure you don't drill into the needle itself.