Back around 2012....while the President still had some leverage with Congress (a Democratic Senate)....they pursued the Iran Threat Reduction and Syria Human Rights Act.
It's not something that people generally remember or read....but the significance of the congressionally passed act is that Iran can only removed from the State Department’s list of terror sponsors, if the President certifies they've permanently ceased the pursuit of weapons of mass destruction.
Oddly, in public....Iran has said that it just won't stop supporting terror operations and they won't really stop their effort to build nuclear weapons. You can't certify much without looking awful stupid.
Naturally, you'd stand there and ask.....how exactly does this President's recent treaty with Iran now work? The answer? It won't work.
If the President had done what was a true-treaty and the Senate voted upon it the normal way to approve it.....then no one would say much. But it was not developed as a treaty, and since they didn't approve it.....it's not a treaty.
How things move ahead?
Unless the House and Senate go and undo this law passed in 2012....it stands. No American business can do business with Iran because of the 2012 law. Now that the President has done everything to take down the US and EU-supported episode.....businesses could start up trade and make money off Iran. Well....all businesses other than US businesses.
I'm guessing that the French, the Germans, and the British all knew about the 2012 law and were grinning as the President hyped up his great treaty. They can walk in and sign business agreements and make billions. The US? If a single company signs a contract....any idiot could drag them into court....even a state court, and sue them for violation of the 2012 law.
Fixing this? Well....you could executive-action this by Presidential authority but Congress made the law and typically a President can't toss such a law out. He might pretend the law doesn't exist and order the Attorney General not to prosecute anyone, but that won't work in a civil court if someone chose to punish a company for violation of the 2012 law.
So in some ways....as much as the President and his team thought they were really on top of things.....they really screwed up badly. Other than getting Congress to dump the 2012 law....there's no way out. And that won't happen with this President, this House, and this Senate.