I am not a lawyer, but here is what I do know for whatever it is worth.
In most states, it's going to be an as is sale. The only state that I know of where you might possibly have a chance is in MA. If you buy a used car in MA, and it does not pass inspection, you may be entitled to your money back (I saw this on People Court, so you know).
Otherwise, you very likely own the car. You did not have the car inspected before purchase I take it? I am a little surprised you didn't even notice the tires were going to need replacing. This is likely a case of 'buyer beware'