MIA response is dead on correct. So much correct that big dealers like Penske that sell Ferrari,BMW,Porsche,etc will not budge but you still can get a independant to let you pay in full although most go for Visa...but my last transaction the guy who sold the card did not convey the Visa only order to the guy who did paperwork. An entire car on an Amex
Selling a car on a credit card exposes a US car dealer to an additional set of consumer protection claims. Credit cards rights are largely established by Federal law, while car dealers are largely subject to the consumer protection laws of the state in which they are located, and automobiles are often covered by specific laws which the dealers understand very well. Accepting a card for full payment simply takes them into uncomfortable legal territory.