If the credit card was a joint account with a surviving spouse, then the surviving spouse should consider paying the credit card bill so that his or her credit rating is not impacted. If the expense belong to the decedent, the surviving spouse can later be repaid by the estate. The surviving spouse should then stop using the joint credit card and instead arrange to have a card in his or her name only.
Generally, unless it was a joint account or another family member signed off as a guarantor on the account, the family is not responsible for the debt. Further, credit cards are “unsecured debt,” meaning that they are relatively low on the list of order of priority in which debts are paid (though if there are sufficient assets in the deceased’s estate, they do have to be paid).
We have read and heard stories of credit cards companies using tactics that borderline on harassment, to pressure executors, trustees or family members to pay the credit card debt or roll it over into their own name. If you are at all uncertain as to whether you are obligated to pay the debt, consult with your attorney first before making any payments.