Can you sue your credit cards to get out of debt?

To have any chance of winning a lawsuit there needs to be legal precedence and substantiated evidence. Regarding suing a creditor the consumer would need to prove fraud and/or antitrust violation, bait and switch tactics, breach of contract and so on. The clerk of the circuit or district court (depending on the state) can help you obtain the info. you need. Another option is consulting an attorney specializing in consumer/creditor law.

No. You decided to sign the contract, so it is your fault that you are in debt. Maybe you don't know how to save money from all the jobs you had or you work in minimum wage jobs that you decided to use your credit cards to buy things you need or whatever the reason is, your credit cards are not responsible for your debt. You can negotiate with them to lower your interest rate, but you still have to give them the minimum due each month.