There are quite a few issues here. First, it's good that you didn't sign the contract. However, it may not totally absolve you. Your best first step is sending a termination letter. From there, you can expect to receive a collection letter. You will need to send another letter to dispute it and reference the lack of a signed contract. Then, your account may be turned over to collections and negative credit reporting may start. You'll probably want to dispute that, too. You could end up being sued, but there is no way to actually know. It is less likely that they would sue without a written contract, though.
The above statements are provided as general information and not intended as legal advice. Each matter has its own set of unique circumstances that cannot be adequately addressed without consultation. You are strongly advised to hire an attorney licensed to practice law in your state to represent you.