They can send you to collections and eventually they can sue you. Plus, not paying will send your credit into the lowest, possible score. Low credit scores mean you won't be able to apply for any other credit cards, any car loans, a house, any sort of financing for anything - furniture, any rented apartment, department store credit cards, anything with financing. I really urge you not to go down this road.
If possible, you need to get a job or get someone in your family to help you pay your minimum payment ON TIME for a year. After a year, then I bet the credit card company will lower your interest amount so you have a better chance of paying it off.
Unfortunately, credit card debt is an awful black hole. You need to pay your way out. All the credit card company will want to protect your credit and get them to work with you is to pay at least the minimum payment on time all the time.
I hope you realize how important this is. Credit card companies report your payment habits to the credit reporting agencies. ALL financial institutions look at this information before they give you any money.
My best advise is to cut up the credit card, stop using it, start paying that minimum on-time no matter what.
Check out Suze Orman at www.suzeorman.com. She has a lot of information on credit scores and credit cards and what to do.