I live in Ca. My husband died in Jan.2010. He has a credit card with Citibank which I was an authorized user. When I contacted Citibank that my husband had passed away, the informed me that the estate is responsible for the debt. I am the one handling the estate. The only funds are from an insurance policy which I am the sole beneficiary. There are not enough funds to apy all his debts. What is my responsibility toward this debt. Should I continue to pay the minimun payment?

You will never get his estate closed via the courts until all debits are discharged. Sounds like you should get an attorney to assist you with your duties as executor.