Am I responsible for the accrued medical bills from my deceased spouse?

Your husband's debts that you are not a privy to by way of contract are not yours to bear.  However, if your husband's estate went to you, the creditors are able to make a claim on the estate for the unpaid amounts.   In your situation I suggest that you stop paying for the meidcal bills.  the medical providers are likely going to turn the bills over to a collection agency who will cal you and you can say that the debtor is deceased and provide them with a death certificate so they stop calling.  to the extent that the medical provider obtains a judgment for some unknown reason against you, you may file for bankruptcy and dischage the entire debt without having to pay for any of the bill.