I'll give this perspective...
I left the game when the timeout was called before the field goal, so I missed the exchange after the game. But I sit in the third row of that section with my family, and have done so for many many years. The same can be said for almost everyone in that section. We are passionate UC football fans with many of us having traveled many times to away games and bowl games. Generally, while being loud and cheering enthusiastically, we are still well mannered and do not yell anything but encouraging words toward the players and coaches. In fact, I don't remember the fan in question yelling anything negative during the whole game, or at any other time in any other games. When the team left the field at halftime, and walked under our section, many of us (along with many others in the crowd) did boo the decision not to try and score before the half. After all they did have 48 seconds and all time outs left. There were some words spoken toward TT, mainly questioning that decision not to try and score and about his desire to let the team play....but NONE of them where profane, mean spirited, or derogatory toward him personally. NONE of them.
The remarks made toward him AFTER the game are TAME in comparison to what I have heard many other coaches (even at the HS level) have hurled at them. As others have said, it's part of the job. Heck, I've heard worse things said to the VOLUNTEER officers in CLUBS I belong to.
BUT....we aren't talking about a pattern of behavior here from TT, at least in regards to using profanity or having direct conflict with fans. He has expressed his attitude toward the fan base in the past, and not in a very flattering fashion, but he hasn't been mean or directed his comments at any single person when doing so. I don't see the need to fire him immediately over THIS incident. I think his performance and lack of success over the last two years is reason enough, and he should finish out the season before being allowed to resign. Let's have some class...more than he has shown...and let him leave on his own terms AFTER the season.