Unfortunately, from the moment that the sales contract was signed, you were most likely legally bound to own and pay for the car described in the contract.
Many people believe consumers have a "cooling off" period during which they can call the whole thing off as if the signed contract never existed (which is true in certain states, and subject to specific restrictions). With a few exceptions, contracts such as automobile purchase agreements do not offer a cooling off period. So, the lender is on sound legal footing refusing to allow you to rescind the agreement. The facts surrounding the verification of your employment don't help you because it is not the lender's duty to make sure you can meet your obligations that you voluntarily undertook when you applied. However, you should still call the finance company directly and explain that you have lost your job and are unable to pay this new obligation. The finance company, not the dealer, is who will suffer if you default on your loan, so they may be willing to help you.
If this strategy does not work, you may want to see an experienced bankruptcy attorney for advice. An attorney will be able to educate you on all consumer issues, not just bankruptcy. Some states have a generally more liberal rescission policy that your attorney may be able to advise you about.
If you simply return the vehicle and stop making payments, the finance company will likely consider the matter a voluntary repossession. The lender will auction the vehicle, probably for a lot less than you paid for it, and you will then be responsible for the difference between the loan amount and the auction price, which is called a "deficiency balance". The lender will probably attempt to collect the deficiency through standard collection tactics, such as referring the account to a collection agency. They could also sue you for the deficiency and obtain a judgment which they could then enforce through wage garnishment or bank levy, if allowed by your state law.
Even if you surrender your vehicle to your lender voluntarily, the lender has the legal right to collect on any balance remaining on the debt after the car is sold at auction. This type of debt is referred to as a deficiency balance. The creditor may even file a lawsuit against you to collect on the unpaid deficiency balance. You should therefore only proceed with a voluntary repossession if you truly cannot afford the loan, as you will likely still owe the lender a significant amount of money, even after you no longer have the use and benefit of the property.
A deficiency balance is an unsecured debt, which the law treats the same as credit card debt, a payday loan, or medical debt, among other consumer debts. To see your rights and options for resolving the deficiency balance, read "Collections Advice."
Again, I think you should consult with an attorney to learn about your rights as a consumer and the options available to you to resolve this situation.
Best of luck,