While you can generally use a prepaid card to pay for a rental when you return the car, the big car rental companies in the US generally do not accept prepaid cards in place of a deposit when you rent a car.
You can either apply for a genuine credit card ahead of your trip (compare Swiss credit cards here).
Some of the major rental companies and many smaller rental car providers let you pay your deposit in cash in place of charging it to a credit card. But at the big-name providers in particular, you will usually be required to provide additional information such as copies of your incoming and outgoing airline tickets when you put down a cash deposit.