Years ago, I recall reading about the challenge to NAFTA, some arguing it is a "treaty," and thus wrongly negotiated. Seemed to me like a treaty (think commercial treaties of yore). A question, with various comments (including mine -- see especially the FAS links), involving a future President abrogating it is discussed here. Whatever the accepted rules, personally, generally think if two parties (Senate/President or Congress itself/President) requires entry, it takes both to exit, since revocation is in effect a new (opposite) agreement or treaty. Here there are rules and the President has delegated discretion. A lot more there.