There is a big difference between who you pay the down payment to and who you make car loan payments to. Your down payment is paid to the DEALER. Your car payments are paid to the LENDER. Your obligation to both is wholly separate.
For example, let's say you agreed to pay a $3,000 down payment but only had $2,000 at the time of sale and agreed to pay the balance of $1,000 in $200 payments for five months. This is your agreement with the DEALER and the dealer has the right to get paid - on time.
At the same time that you are making payments to the dealer, you need to make your car payments to the LENDER. If your car payments are $300 per month, then for the first five months of car ownership you will be paying a total of $500 per month for the car - $200 to the dealer and $300 to the lender.
What happens if you miss a payment?
Once the car loan is in place, the LENDER has a secured interest in your vehicle. You will be listed on your DMV registration card as the Registered owner and your lender will be listed as the legal owner or lienholder. What this means is that only the lender has the legal right to repossess your car for failure to pay your car payments and sue you for the balance on the loan.
Once the lender is listed with the DMV as the legal owner, the dealer no longer has any secured interest in the vehicle and therefore has no legal right to repossess it if you fail to pay the dealer for the balance of the down payment. However, the dealer does have the legal right to sue you for the money you owe.
This doesn't mean that the dealer won't try to repossess your car illegally, which puts you in a terrible position with the lender because you are still obligated under the loan agreement to make your car payments on the loan for a car you no longer have possession of.
Seriously consider if you are financially able to make two payments at the same time.
Lenders decide whether or not to finance a vehicle loan based on what is written on the sales contract. If the sales contract shows that you have made a $3,000 down payment, but you actually only paid $2,000 and are going to make five more payments of $200 each to pay the dealer, the dealer is misrepresenting to the lender what the actual terms of sale are. If the lender knew that you were obligated to pay $200 per month to the dealer at the same time that you are making a $300 per month car payment to the lender, the lender may have refused to fund your car loan. If your income shows that you can easily make a $300 per month car payment, but not a $500 per month car payment, the lender would be taking too great a risk that you will default on your car loan. Rightly so.
Your best choice is to buy a car with only the amount of down payment that you actually are able to pay in cash at the time of sale - no deferred down payments.