Marty Lederman at Balkinization has confirmed, The Iran JCPOA ain't a treaty (or an executive agreement, for that matter). See this pdf from the State Department.
The Joint Comprehensive Plan of Action (JCPOA) is not a treat or an executive agreement,a nd is not a signed document. The JCPOA reflects political commitments between Iran, The P5+1 (the United States, the United Kingdom, France, Germany, Russia, China), and the European Union. As you know, the United States has a long-standing practice of addressing sensitive problems in negotiations that culminate in political commitments.
The success of the JCPOA will depend not on whether it is legally binding or signed, but rather on the extensive verification measures we have put in place, as well as Iran's understanding that we have the capacity ro re-impose -- and ramp up -- our sanctions if Iran does not meet its commitments.
Everything in the JCPOA and its annexes are commitments Iran made, and must keep, to remain in compliance. If Iran breaks these commitments, we can snap back both unilateral and UN sanctions.
The part Lederman is confirming is that Republicans knew of this arrangement, and aren't arguing the constitutional aspects of such a commitment:
But here's what's so interesting to me, and what I meant to stress in my last post: Despite the general, deep polarization Mark describes, there is no such polarization on the constitutional questions that Jack and Sandy raised, because of a remarkable settlement that has been established over the past 100 years of U.S. foreign policy and diplomatic practice--a settlement that, I might add, was unknown to approximately 99% of all law professors (myself included), ignorant as most of us are concerning the way that the government actually functions in foreign affairs. (For much more on the extraordinary disconnect between the academy's hidebound, "received wisdom" views and the actual constitutional practice of foreign relations as conducted by the U.S. Department of State, see Harold Koh's terrific 2012 Ryan Lecture here at Georgetown.)