Here's how the hills roll on from my view:
If we get an at large bid to the Dance, Billy stays, assuming he makes the second round. A first round loss in either tournament will only underline the arguments for his dismissal.
If he doesn't put together a very serious run in the NIT, he won't help his prospects. I bet he wishes he'd signed that contract now!
My gut has spoken, and not just about dinner, either. (hehehe)