From Disney's website
"Changes to Reservation- For a change made 29 days or less prior to arrival that results in a change in the package price, a change fee of $50 per package, plus any change fees assessed by hotels and other suppliers, will be charged. Such change fees must be paid in addition to any increase in the package price resulting from the change. If air travel has been ticketed, Guest will be responsible for any increase in airfare as well as the change fee assessed by the airline."
This is for packages, don't know if a 'room only' reservation is different or if doing it at check in would be different. I expect it might since they might not be able to rebook the more expensive site, at least for that night. You probably ought to call Disney to see what they say.