>>bright+(OP)
The short answer: it's really complicated. In a broad stroke, a treaty agreement is roughly akin to Congress passing a law, but the roles of the treaty itself versus enabling laws depends on several factors such as "is the treaty actually a treaty?"
As it pertains to your question, the Constitution (and its amendments) are the supreme law of the land, and a treaty stipulation that requires the government to do something unconstitutional would have no legal effect.