The answer to this question depends on the specific terms and conditions of the agreement you made with the dealership. If you have a written contract that states that you are responsible for making payments starting the next month, then the dealership may be able to repossess your car if you do not make those payments. However, if you have a verbal agreement with the co-owner that you will pay 60 days later, then the dealership may not be able to repossess your car unless the co-owner fails to make the payment.
In general, it is important to make sure that you have a clear and written agreement with any dealership or lender before you purchase a car. This will help to protect your rights and ensure that you are aware of all of the terms and conditions of the agreement.