A couple things to note:
When the CM swipes the card to activate charging privledges, nothing is charged to the card. The computer just puts a hold on $1 to verify that the account is valid. You may use any card (Debit, gift card, credit card) as long as it has the Visa, Mastercard, Amex, Discover logo on it. Disney also accepts JCB, Diners Club, and maybe one more.
Your card is not charged until you reach your resort credit limit, or if you come close to it. Depending on the classification of the resort, the credit limit can change.
One thing to note... if your bank has a limit to the amount you can use your debit card per day, and your resorts limit exceeds the one set by the bank, there is a way around it. Two, actually.
The first, is to monitor your charges... For example, you have a $350/day limit. You can then call the front desk on your phone (or visit the front desk) and each day as needed, you authorise them to make a $350 payment (regardless of if your balance exceeds that... you can also have them take a payment that exceeds your current balance)
The other way is to have the resort change your credit limit to whatever your bank limit is. (yes, this is possible... they can lower it, just not raise it)