It would take a few things.
He'd have to lose at least two more games. If he lost to Kentucky and Vandy in the same season, that would be pretty devastating. I don't even think Dooley did that, did he? This alone wouldn't get necessarily get him canned, but you'd have enough folks disgruntled that some organized efforts would begin to stir among the boosters.
After that, it comes down to timing. I think there'd have to be a big splash out there that all were VERY, VERY confident, if not certain, that they could land. They'd almost have to have an agreement in principle before they dropped the hatchet.
If the big splash was in hand, I think the boosters would scrape up the money to walk CBJ. I don't think they'd be on board if it was simply a "fire Butch and see who we can get" sort of situation. We're probably another year or two away from that.