Can executor sell house to heir to pay off mortgage?

Generally executors have broad power to act in the bests interests of the Estate of the Decedent.  With great power comes great responsibility and, here, possiblygreat liability. 

An executor has the obligation to pay off the debt of the estate with the assets.  If you are aware of the credit card debt you have an obligation to address it and not just ignore it.  It depends on the state law how you need to address the debt.  Sometimes a Notice needs to be sent out advising of the Probate and the right to file against the estate.  Some states require publication.  Each state is different.  Most have a time frame for relieving the estate of debt if proper notice has been given and the creditor fails to act in time.

As for the house, which appears to hold equity to deal with other debts.  Without a Court Order, if the Executor acts wrongly, he is open to liability.  If there are other heirs they can sue as well.

I would seek legal counsel with the Probate action to best protect yourself.  If you choose to sell the house for below market value and everything else is the estate has been properly accounted for I would seek Court approval of the sale.  This way you are protected.