Here and here, for a conversation they had in a car and put on Facebook.
Barton refers to "4 types of law," which is Aquinas. [Blackstone had 6, but they're similar.]
Aquinas recognizes four main kinds of law: the eternal, the natural, the human, and the divine. The last three all depend on the first, but in different ways. Were we to arrange them in a hierarchy, eternal would be at the top, then natural, then human. Divine law is not in conflict with natural law, but it reaches human beings by a different route, revelation.
Barton usually has something substantive in mind, although what comes out is often a jumble. However, his point here could be whipped into shape.
Elsewhere, a correspondent cites the "supremacy clause" of the US Constitution:
Article VI: This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding.
But that's circular. The Constitution's supremacy clause does not grant to the central government powers it's not specifically given. It is not the supreme ruler of the land, only the highest legislature.
The Constitution was conceived as giving only certain enumerated powers to the central government. The supremacy clause, the "law of the land," applies only to what the central government is constitutionally empowered to do.
Of course, today the federal government claims absolute power over every facet of our lives, but this does not mean it's a legitimate power, nor are we bound by any moral law to bow to it against our consciences--a moral fact implicitly in the First Amendment's free exercise clause.
"Upon these two foundations, the law of nature and the law of revelation, depend all human laws; that is to say, no human laws should be suffered to contradict these."--Blackstone
“A just law is a man made code that squares with the moral law or the law of God. An unjust law is a code that is out of harmony with the moral law. To put it in the terms of St. Thomas Aquinas: An unjust law is a human law that is not rooted in eternal law and natural law.”---Martin Luther King
"That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness."--Jefferson, et al.
Barton [and Kim Davis] will lose before the power of the state, which has the biggest guns. But his argument is both timeless and tenable. It's disappointing that their critics are so blinded by their animus against Barton and Beck that they have forgotten the Founding principles. We have the natural right to resist tyranny in all its forms, even "legal" tyranny.
Lex iniusta non est lex.