My sense is that there could be some pushback from players, recruits, a few fans, and potentially Groce's allies in the administration and coaching community if he was fired after making a big push to finish the year with 24-25 wins and deep runs in both the BTT and NIT. Not a huge deal, though. A few people might say, "he deserves another year," but JW would take recourse to, "we expect to be in the NCAA tournament perennially unless there are considerable mitigating factors." For me, releasing him before the NIT (in the event that he finishes 9-9 in the B1G and wins a couple of BTT games) is more about getting out in front of the coaching search and communicating a plan quickly to recruits that may request a release. Outwardly a statement of purpose and internally an organizational reset.
However, if Groce finishes at 8-10 or worse, I'd personally want to let him go before the BTT because the auto bid would then be the only scenario where UI would make the NCAA tourney. In that case, I'd want to eliminate the potential mess (from my perspective) that could come if Groce won the BTT and won a game in the NCAA. You'd suddenly be looking at a 23-win team that won a conference tournament championship, won a tournament game, and had a top-15 recruiting class on the way. I think it would be very hard to let Groce go at that point, but I'm already convinced he's not the right man for the job - I don't want a lucky run to save him (and probably necessitate an extension).
My vantage point is this: another losing season in conference play coupled with the impossibility of an at-large bid (i.e. entering the BTT off the bubble completely) is automatic grounds for termination. I wouldn't want an anomalous winning streak to create tricky dynamics, so I'd bounce Groce right away and bring the coaching search out of stealth mode. However, if Groce somehow finishes 9-9 in conference, wins 2+ games in the BTT, makes the NCAA tournament, and wins a game there...well, he gets extended. Fair is fair.
This is just an academic exercise - I'm confident we'll lose a game between now and the second round of the BTT and Whitman's decision will be made for him. Just thinking about different improbable scenarios.