Is wife responsible for deceased husband's medical bills in NJ if there is no life insurance?

The availability of life insurance doesn't change the situation. It is the assumption is that the wife inherits at least half, if not all, of the husband's assets. But the estate has to liquidate all assets before they can transfer them to the spouse. One way or another, the spouse ends up paying the debt. The spouse has some right in all real property owned by the husband. If the assets are not enough to cover the debt, the real property may have a lien placed against it to cover those debts.