In a word: No.
You're only responsible for your parent's debt if your name is on the account in question as a joint account holder, not just as an authorized
user of the account. If you haven't already co-signed any accounts with him, make sure you don't.
Even if you hold a power of attorney appointing you as your father's designated decision-maker, you're still not responsible for his debts unless you're found to have illegally commingled money from his accounts and yours.
The bottom line is that your father's debt isn't technically your problem, but there are steps you can take to help him resolve his situation without ruining your own credit or taking on his debt yourself.
If he owns his own home and doesn't have a large mortgage, he may be a good candidate for a reverse mortgage, which can eliminate his monthly payment and give him some breathing room to pay off debts and deal with other expenses.
If his debts are unmanageable and a reverse mortgage isn't an option -- if he's already living in a nursing home or other managed care facility, for example -- it may be time to consider filing for bankruptcy protection. Bankruptcy may be particularly appropriate if there's nothing left in the estate to protect and you want to keep creditors from hounding your father day and night.