The biggest argument against Croom is that the only successful unit on his teams has been his defense. He's an offensive coach. If the unit of your expertise has never been a strength of the team, then you're probably not that good of a coach.
At least with Cutcliffe, our major problems were usually on our defense. Offense was never an issue. Tubberville for another example is a defensive coach. Defense is usually the strength of his teams. Petrino is an offensive coach, and the strength of his teams historically has been offense. Same with Nutt.
I don't know that I've ever seen a head coach who has had more trouble getting his expert side of the ball to perform. When your background is offense, and your offense has never performed at all, it makes you wonder. You still have a long season ahead, and I believe that your defense will give you chances to possibly pull off some surprises and possibly still get you to 6 wins and a bowl. However, even if you were to come back and go 6-6 or 7-5, I don't see how Byrne couldn't be concerned with the lack of offensive production.