Put the ball back in your court and refuse to drive the vehicle off the lot until the financing is in place and finalized to the terms you have approved and can live with.  Once you have copies of the car loan application, buyers agreement (which must also be signed by the car dealer representative) and receipt for your down payment you legally have right to that vehicle and it cannot be sold out from under you.  If they were to do that you have the right to sue for breach of contract which is a business tort and it would be easy to find a lawyer in your town or city whom would gladly take that case on a contingency basis. 

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The best part of refusing a spot delivery is that you can now have buyers remorse.  If you go home and find a better price elsewhere or just decide it wasn’t as good a deal as you thought (Tip – this is usually true.  You can always find a better deal.  The car salesperson and car sales manager will lie to you and tell you this is the best deal ever – it never is, they just want you to buy,  sign on the dotted line and take the spot delivery thus greatly fattening the car dealers wallet). 

If you get buyers remorse and didn’t take delivery of your vehicle than you legally didn’t buy the car and the car dealer must refund any monies paid down or return any traded cars.  Some states have wisened to the bad practices of many car dealerships and the thousands of customer complaints with respect to spot deliveries and have made them illegal.