I would recommend that you consult with an attorney to have the contract reviewed. It is difficult, if not impossible, to answer your question without reviewing the contract and understanding the circumstances completely.
Whether they have the right to make you sign a new contract probably depends on the sales paperwork you signed. Look at your sales paperwork for a document that is often called a “Spot Delivery” or “Bailment” Agreement. That's a paper that says what how long the dealer has to set up the loan and what happens if they don't get it done on time. It usually says they have 3 to 30 days (usually on the short side of that total) and that if they can't set up a loan then you have to give them back the car and maybe pay for the mileage you drove on it. Whether or not you get your trade in or down payment back should also be covered. This whole process is called "dehorsing" by the car dealers themselves (you can read a Car Dealer's Slang Dictionary at this web page: http://ohiolemonlaw.com/car-dealer-dictionary.html) and doing it can be a violation of most state Unfair & Deceptive Acts and Practices laws (these are called “Udap” laws by Consumer Law lawyers). If your amount being financed is less than $25,000 (to find out just look at your finance contract's "federal box" where key finance numbers are stated) then doing this to a consumer very likely is also a violation of the federal Truth In Lending Act too (that’s a consumer protection law that deals with financing). Some states (like Ohio) also have a law that specifically applies to car dealers doing this sort of thing. If you don't have any spot delivery document in your deal and there is nothing on the finance contract that says it is contingent on financing approval and it says on it that the dealer (by its name) is the "creditor", then your deal may be a final contract and if the dealer can't get a lender to finance the sale for you then legally the dealer is probably stuck having to take your loan payments or else let you out of the deal, but of course they won't tell you that and they, in fact, will probably say they don't have to at all. You need to talk to a local Consumer Law attorney who deals with this kind of case (it's called "autofraud" or car sales fraud). Call your local attorney's Bar Association and ask for a referral to a Consumer Law attorney near you or you can go to this web site page for a Free Online 50 State National List of Consumer Law Lawyers (http://www.ohiolemonlaw.com/ocll-site/ocll-locate_local.shtml) and find one near you (lawyers don’t pay to get listed here and most of them are members of the only national association for Consumer Law lawyers, NACA.net). But act quickly because for every legal right you have, there is only a limited amount of time to actually file a lawsuit in court or your rights expire (it's called the statute of limitations), so don't waste your time getting to a Consumer Law attorney and finding out what your rights are. If this answer was helpful, please give it a thumbs up below. Ron Burdge, www.CarSalesFraud.com