The parks are virtually deserted the week before Thanksgiving week. On Friday evening before Thanksgiving, the hotels begin to fill, by Saturday parks are much busier but not too bad. Sunday the crowds are large and beginning Monday of Thanksgiving week (IMHO) things are a zoo. The crush continues thru Thanksgiving weekend and by Monday after Thanksgiving the change is phenomenal...back to quiet and low/no lines.
In other words the weeks before or after Thanksgiving are great, the week of, is a mob.