to put this in a better analogy, if you can't pay a car loan do you try to work out better terms before you stop paying, or what until about to go into default and demand better terms or you will destroy the collateral property (the car)? .......
You left out the other option.
Send the car back (admitting the mistake in borrowing over your income in the first place) or sell it. Pay the balance and buy a car within price range.
Either way your credit takes a hit. Mark how is it Obamas?