If a President signs a treaty, and if the senate ratifies it, then that treaty becomes the law of our land.
United States Constitution, Article VI, 2nd paragraph
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.
Also see Article II. A treaty needs consent from 2/3rds of the Senate, which is even more than the super-majority required for cloture.
Will Obama get 67 Senators to comply?
-PJ