> the treaty violates the U.S. Constitution

I am not a constitutional law expert, but I believe that under article 6 section 2 (the supremacy clause) treaties are held to be equal to the constitution. Thus, there is a very high bar for a treaty to by nullified based on contradicting the constitution. There is very little case law on this, and I believe the only instance in which an international executive agreement (not a treaty) was thrown out by the Supreme Court was Reid vs Covert. In that case, it was throw out on the grounds that it violated 5th and 6th amendment protections of Americans in foreign countries.