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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, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
I think this is the clause they intend to use to hold treaties equal in law with the Constitution. As I read it treaties are superior to State law based on this clause. That alone is scary stuff.
I wouldn't worry too much about that. Treaties are superior to State law since they fall under the Supremacy Clause whereby (Constitutional) Federal laws trump State laws. A treaty can't be used as an end-run around the Constitution- a treaty that infringed on First Amendment rights, for example, would be just as unconstitutional as a law that did the same.