We were there the first week of June, so things might have calmed down a little since then. However, we went to the end of the line for a show starting early afternoon (can't remember the exact time) about 30-35 minutes before the show started, and were told that we would not make into that showing. We were not staying at AK all day, so we skipped it and headed back to the resort.
That may have been the exception rather than the norm, but the day we were there, I would say you would have had to be in line at least 45 minutes early to get in.