keri,
I'll take a guess here: you are a Brit and trying to use a Visa DELTA card (debit card)?
I've had this problem before, they won't allow you to hire a car without a credit card. You can do it, but its a bit more complicated. I've done it with Alamo/National - you have to basically submit to a credit check. Best bet is to ring the reservations now and see what they'll offer you. If its a debit card, say so - and then see if you can be credit checked or similar. That credit check then stays on your file at Alamo/National for a period of time.
I got fed up with the hassle and just use the credit card now, but it always seemed daft that with my debit card I HAD to have the money in the account for the transaction, whereas a credit card just seemed to be a way of building my debt up - but I think there is something where having the credit card means they can get the money if you leg it with the car or similar.