After your death is your daughter responsible for credit card balance?

The estate of the person who has died is responsible for any debts. If there is not enough money in the estate to pay these debts then the people or companies to whom the debts are owed, simply never get paid. The descendants of the person who has died do not have to meet these debts unless they are party to the debt agreement (i.e. they signed the debt agreement too - i.e. the credit card is held in joint names).