Not talking about that aspect (supremacy of it vs constitution), but this and related stuff with treaties vs federal law:
> The enforceability of treaties was further limited in the 2008 Supreme Court decision in Medellín v. Texas, which held that even if a treaty may constitute an international commitment, it is not binding domestic law unless it has been implemented by an act of Congress or is itself explicitly "self-executing".[26] Law scholars called the ruling "an invisible constitutional change" that departed from both longtime historical practice and the plain language of the Supremacy Clause.[27]
