I rent from Hertz with my debit card all the time. It's a VISA debit card from my bank, nothing special. I've never had to do anything special when renting the car - in fact I've never even had to swipe the card in person.

Enterprise is the same story except they don't have the fast exit options that Hertz does so you do have to swipe the card - no one has ever said anything about it being a debit.

Any VISA or MasterCard debit card appears identically to a credit card as far as the rental car companies are concerned.