The rights and obligations of parties to a contract are not defined in terms of the performance of the parties, unless it is. The first thing to do is look at the contract and see if anything says that payment can be suspended until the goods are delivered. I assume there is no such clause. So it appears that one party (the dealer) is in breach, and the question is what you can do. You may ignore the breach, sue over the breech, or you may negotiate for an alternative outcome. The first solution is, long-term, unsatisfactory, but easiest. The second solution is most complicated, and may be unsatisfactory (it depends on whether walking away from the deal is a viable option). The third solution, when paired with discussion (with the dealer) of the second option may be easiest and most satisfactory (e.g. "payments are not due until you hand over the car").
Two additional complications related to the fact that this is a car sale are (1) there may be state-specific laws related to delivery of the vehicle and (2) a loan from the dealer is not the same as a loan with a third party, arranged by the dealer. Failing to pay the third party is unambiguously a bad idea. Point 2 does, however, also impinge on your ability to negotiate a delay of the payment (it's out of the dealer's hands?). The question you need to know the answer to is, where in what contract does your obligation to pay come from. and is it dependent on delivery of the item, or just transfer of ownership without taking possession? If the contract says that payment is due on delivery, you are not required to pay until they have performed.
In other words, it almost entirely depends on what the contract(s) require(s).