You sell a house and can not pay off the mortgage will you be liable for the remaining dollars owed?

Well, you can't sell it if you can't pay off the loan against it. (You can't provide clear title to the buyer unless the liens are paid off at the closing and no new mortgage he needs can be put in first place of the existing one).

Yes your responsible to pay off the loan in full. However, another arrangement (a short sale) may be able to be worked out with the lender. If your in bankruptcy there may yet be other alternatives.