My mother is dying and has consumer dept in her name only. Will my father (still married to my mother) be responsible for the debt once my mother has?

Typically, debts of the deceased are paid out of the proceeds of their estate; families do not inherit such debt.  Unfortunately, Washington is a community property state, and as such there is a presumption that debts are for the benefit of the community (family or couple) and that makes the community liable for them.  In other words, your father would be obligated to pay off your mother's credit card bills.

However, as a practical matter, the credit card employees probably would not know whether he was liable for the debt; they only have names on accounts to go by, and are likely not in a community property state so they aren't necessarily aware of the law.

Once your mother passes and her estate is probated, notify her creditors.  Chances are more than likely that this will end the matter.  To the extent it does not, then your father will have to work out some type of arrangement with any creditors still insisting on repayment.  Worst case, he can consider bankruptcy.