Who is responsible for my deceased mothers credit card debt?

I am sorry for your loss.

Generally, if a person dies and leaves behind a string of loans and credit card bills, then you are not responsible for the payment of these debts unless you guaranteed the debt. If you acted as guarantor when the deceased took out the credit, then it is up to you to assume responsibility for the loan, as you have legally signed to state that you would do so. It is the Estate of the decedent that is responsible for paying the debt.

Did your Mother leave a Will?  Then the executor has the fiduciary responsibility of gathering assets and debts and paying the debts from the assets.  Same for an Administrator who is appointed when no Will is present.

One thing to remember is that most creditors will make a claim against the estate of the decedent for any monies owed rather than approach a relative of the deceased. This means that the relatives may still end up paying for the debts in a way, since the more debts there are, the more money will have to be paid out of the estate before the beneficiaries receive anything. 

What needs to be done in terms of the estate depends on how the house is held by the owners in the deed.  What the credit card companies do will depend on how much trouble they want to go through to get a judgement against the estate, which can be filed and recorded and found when a title search is done before you transfer the house.  The debt would have to be paid then.  Keep in mind that there may be interest as well which could be substantial.

You should take all the relevant documents to an attorney in  your area for consultation.  Good luck.