What if the Dealer wants me to sign a Second Contract?
In a word, don't.
Nothing requires you to sign a second contract. If the dealer cannot do the deal on the terms of the first contract, then something was wrong at the outset. If he cannot finance you on the terms of the first contract, it is very possible he knew it at the time. Some dealers just want to get the customer in the car, get him or her to drive it home, show the family and neighbors, then do what in bad sales practices is called "the take away". It is also called setting the hook. The customer now wants the car is used to it and does not want to be embarrassed by having to tell friends and family he or she could not qualify for the financing. Some of the unscrupulous dealers will tell the consumer "you have to come down and sign a second contract." No you don't.
I have seen the interest rate doubled on the second contract. I have also advised clients to tell the dealer no, that they expected the dealer to honor the first contract. What do you know? They did. What does that tell you? It tells me that the dealer was not truthful, and was probably only trying to make more profit by increasing the down payment, and/or the interest rate.
Contracts vary and each contract must be read to determine your rights. You should consult a lawyer regarding contract questions. Talking to a lawyer early is important to protect your rights. If you have a problem with the dealer you should consult a lawyer in your area. If the dealer repossesses the car, you may have a claim and should act promptly.