Talk to the manager at the dealership and explain why you cannot go through with the purchase. The car dealership's manager has the ability to void your purchase contract. While there is no guarantee that the manager will do so, if your story falls on sympathetic ears, the manager may just tear up your contract.
Read through the purchase contract for a return policy. A common consumer misconceptions is that you have three days to return your vehicle after purchasing it. While dealerships are not required to grant you this provision, some do in effort to further customer relations. If your contract contains a three-day right of revision, you can get out of your signed contract by returning the car within 72 hours after purchasing it.
Demand that the dealer take the car back under your state's lemon law statute. All state lemon law statutes differ, but in general if you have had the car repaired more than four times for the same issue and the issue remains, you can escape your contract due to the car's status as a "lemon."
Refuse delivery of the car. If you have a certain vehicle in mind but the dealership does not have the car in stock, it will order it for you. If you change your mind before the car arrives, refuse delivery of the vehicle and offer to compensate the dealership for their storage fees and the documentation fees necessary to prepare your paperwork in exchange for voiding the contract. Provided you did not finance the vehicle through the dealership, the dealership may accept your offer since it recovers a profit on the vehicle and can still sell it to another customer.