Should I be able to use a Visa prepaid debt gift card for iTunes purchases?

Typically no. Such cards usually don't have a billing address associated with them which the iTunes Store requries for any credit-type card. If your card has an associated address, you can try entering in the card and see if it will be accepted, but most likely it will not.

You can see the valid payment methods here:

http://support.apple.com/kb/HT5552

Regards.