First of all, I am sorry to hear of your mom's condition. If you are only an authorized user, then you will not be liable for the credit card debt. In this situation, why not be safe and have your mom remove you as an authorized user? That is a cheap and easy solution for you. That way the creditor, or worse a collection agency, cannot harass you for payment. If your mom has any assets of value, then you would have to pay the credit card company out of the estate. It sounds like your mom does not have any assets.
Take good care of your mom and enjoy your time with her.
Please note that although this answer may provide information concerning potential legal issues, it is not a substitute for legal advice from qualified counsel. You should consult an attorney for individual advice regarding your own situation. Answering this question does not create any attorney-client relationship between you and Kelly Zinser, Partner at Olenicoff & Zinser, PC.
According to a major court case that was published in May 2010, the credit card user is not liable on the debt, only an account holder is. I blogged about this and provide a link to my blog, below.
I would advise much caution about sending any personal checks with your name to the bank, as they sometimes simply add the check payer to the list, and you may start getting bills in your name. When she does pass, they will try to stick you with the bill, unless you have a probate, which can be costly to handle properly.
You may want to have your mother file bankruptcy before she dies, to clear out all her old debts, to ensure that she leaves you with nothing to worry about. What little assets she as are most likely exempt and the filing fee for bankruptcy would probably be less than your monthly payments on this credit card. There are attorneys who can handle this for you at a considerable discount, especially since your mother's assets and debts are so few and simple to put on the schedules.
Check Avvo's "find a lawyer" tab for bankruptcy attorneys in your area.