I don't understand the debit card thing. You can only run up a bill for the amount youve got in your checking account.
And it's almost impossible to rent a car/reserve a hotel room etc. with a cc.
So ...
Open a free checking account with a debit card associated with it. Dump a couple of hundred bucks in it (to cover the "hold back"). At the end of the stay, pay in cash.
Also, those pre-paid cc's can be used, too. I know folks who can't get a regular card ... they pre-pay for one of those and it makes their travelling a lot smoother.