“Article six of the U.S. Constitution:
...”and all Treaties made, or which shall be made, under the authority of the United States shall be the supreme law of the land...””
It’s well settled that the Constitution needs to be intercepted in such a way as to avoid conflicting clauses. Therefore a treaty cannot be contrary to any part of the Constitution. So just as any law passed by Congress is assumed null and void from it’s effective date if it violates the terms of the Constitution, any treaty must be treated in the same way.
One clause of the Constitution cannot nullify or alter another of itself or in any action done under it’s provision. Or, to put it shorter, the Constitution has no poison pills.