http://en.wikipedia.org/wiki/Reid_v._Covert
Reid v. Covert, 354 U.S. 1 (1957), is a landmark case in which the United States Supreme Court ruled that the Constitution supersedes international treaties ratified by the United States Senate. According to the decision, "this Court has regularly and uniformly recognized the supremacy of the Constitution over a treaty," although the case itself was with regard to an executive agreement and the treaty has never been ruled unconstitutional.
Even if such a treaty were passed by 2/3 vote in the Senate, it would probably be unconstitutional and therefore invalid.
We hope.
But how much damage could an administration like the current one do until that determination was made by SCOTUS - which assumes they would indeed find it unconstitutional.
Once done, history shows undoing is difficult if not impossible.
Once the .gov gets power they don't ever, ever give it back.