You can back up a room charge with travelers checks, cash, Disney Dollars, credit card, or debit card (with VISA/MC logo).
Those above-stated limits for room charges by level of resort are UPPER limits -- you can set the room charge for any amount up to and including that amount.
LACK OF HORROR STORY:
When you use any sort of plastic to back up your room charge at a WDW resort, they do not pre-charge your account, and they do not place a hold on your account. In fact, they don't even check to see if you have enough in your account! They "run" the card just to make sure it is tied to an active account. But they absolutely definitely don't pre-authorize anything or have a hold placed on anything. For example, let's say your debit card is tied to your checking account. Let's say you have $3,000 in your checking account. You check in at your resort and set up a $1,000 room charge. You can call your bank every day, and every day you will still have a $3,000 balance in your checking account (if there was no other activity, of course), because Disney placed NO HOLD on your account.
Same thing if you have a credit card with $3,000 available credit. If you authorize a $1,000 room charge, you can call your credit card company every day, and every day you will still have $3,000 available credit, because Disney placed NO HOLD on your account.
If you reach/exceed your room charge limit, then your credit/debit account will be automatically charged. But as long as you don't reach/exceed your limit, nothing will be charged until about 3:00 a.m. on your check-out day. You can also go to the front desk before you hit the limit, and pay down the account through any other means you want. Also, you can go to the front desk at any time and get an up-to-the-minute printout of your room charge activity and current room charge balance.
Personally, I've not read even one single horror story about using a debit card to set up a room charge. And I've done it twice myself and it's worked according to plan. Any chance you have a link to these horror stories???