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)