Well, after researching it appears that how the President decides to label it- treaty vs agreement. If it is labeled an agreement, Congress loses control over it. Oh, what fun!
BUT Congress gets a right to a yes or no vote, and once again, BUT the President can veto that vote, unless emough Dems are willing to vote to overturn his veto to a no vote by Congress.
It just gets more & more fun, doesn't it?
I am sure Iran has been told just follow Kerry's lead, you can do what you want and this deal will never present itself again, so go for it.