Does my family have liability if my advance directive instructs no heroic measures or life support?
No. Every competent adult has the legal right to choose what medical treatment he or she wants or does not want. Some people, for example, refuse medical treatment because of religious objections, and this is their legal right. Every state in the United States recognizes a living will, which is a document that says what life support techniques and equipment a person does or does not want used in case of an emergency where the person is incapacitated. A living will is one document included in the category Advance Directive for Health Care.
In following your living will or Advance Directive for Health Care your health care providers and family will be carrying out your wishes for your health care. As long as you were competent when you executed (signed) your living will or Advance Directive for Heath Care, your health care providers, family, and the representative you named in your Directive are all legally obligated to follow your directions. (Though in some states, emergency personnel always resuscitate, and your directive is not applied until you reach a hospital.)
The point is that this is your choice, a choice you are legally and morally entitled to make. No one else can be held responsible, since no one else has the right to take that decision away from you.