You can ask for late check-out, but it will be up to the discretion of Housekeeping on the day you check-out. They likely won't be able to tell you any earlier than that. Whether or not they grant it for you will depend on how many housekeepers are on duty, how many people are checking out, how many are checking in, etc.
If you are traveling during a slow time and checking out on a weekday, they may permit you to stay in the room up to an hour after check-out. I've not seen anything longer than that permitted, however I have heard they may offer additional time for a fee. Many non-Disney hotels have this option as well.
You can always store your bags with bell services at you resort after check-out, so don't feel as though you need to lug your stuff around with you until you leave!