The answer depends on all of the paperwork you signed. Sometimes, dealers make purchase agreements with customers that say "subject to credit approval" or "contingent on credit approval." They sometimes use separate forms saying the same thing. Look through your paperwork for those things. If they did not make the purchase subject to credit approval by the bank, then as a general rule they are out of luck. This happened to me when I bought my wife's van, and the dealership ended up signing a guaranty with the credit union saying they would be responsible for the loan if I defaulted.
If they did make the purchase agreement subject to credit approval, things get trickier since your old vehicle is already gone. If they change the terms in this situation, you have the right to back out of the deal. If this turns out to be the case, I would consult with a local attorney about your options.