This is referred to as "yo yo financing" - it is illegal.
The dealership will sell a vehicle to the consumer under specific contract terms and conditions, then use a pretense (such as the interest rate is no longer available, the credit check came back different, or some other excuse) to threaten the customer into either refinancing the auto under less favorable terms, or into returning the auto and purchasing a more expensive one.
This is a form of fraud. The terms of the contract that you agreed to at the time that you purchased the vehicle are controlling, and both you and the dealer are bound by those terms. If the dealership cannot find a lender to take over the loan, they must service it themselves.
You can (should) report this to the State Attorney General's Office, Consumer Complaints/Protection division (online reporting) so that the attorney general can investigate and take criminal or administrative action against the dealership.
You do not have to change the terms of your purchase, and you do not have to return the vehicle.
As you have already returned the vehicle, you may want to work with one or more of the above agencies, then try working with the GM (or simply contact the GM again directly) and see if they are willing to reinstate the original deal and avoid having you sue them for fraud.