Fans are often too quick to move on from young players, having been burnt by ones who failed to develop and forgetting the ones who did develop. The team is often too slow to move on from young players, remembering the ones who did develop and ignoring the ones who didn't.
There's a fine line between the two. Coaches have to accept the fact that they can't make everyone a success story; you can't make a silk purse out of a sour Costa. Fans have to accept the fact that some players just need time to adapt, especially those who come from smaller schools.
If Dallas had played Romo his first year with the team, he would have put up some pretty poor numbers because his mechanics needed a lot of work, and people would have been screaming for Dallas to move on. Plenty of other players didn't exactly light things up their first year, or even first few, in the league: Bradie James comes to mind; Jason Hatcher wasn't really much until the past couple of seasons. Some come in immediately ready, but others are just "late bloomers."
The fear is that they won't bloom, but I think it's a poor idea to overreact to that fear.