According to their website sections on rental policies:

Alamo

Their car rental debit card policy states:

Alamo only accepts gift cards for final payment upon return of the rental vehicle. Gift cards are not acceptable as a form of cash deposit.

Avis

Their rental car debit card policy states:

Prepaid debit/gift cards are not acceptable methods of credit identification to pick up a car at any location. One of the above mentioned cards must be presented. Prepaid debit/gift cards are accepted at time of return only.

Budget

Their car rental debit card policy states:

At time of pick-up, you may not use a prepaid debit or gift card for the required hold. However, prepaid debit and gift card cards may be used for payment at time of vehicle return.

Dollar

Their rental car debit card policy states:

Prepaid credit cards, gift cards and debit/check cards are accepted for payment at the end of the rental only.

Enterprise

Their car rental debit card policy states:

Pre-pay credit cards are not accepted at any of our rental locations. We apologize for any inconvenience.

National

Their rental car debit card policy states:

National only accepts gift cards for final payment upon return of the rental vehicle. Gift cards are not acceptable as a form of cash deposit.

Thrifty

Their car rental debit card policy states:

Prepaid credit cards, gift cards and debit/check cards are accepted for payment at the end of the rental only.