Been a while since civics, but afaik Morris is not just wrong but very wrong, a fact I find disturbing given his standing in the government.
A President can negotiate a treaty but cannot sign it into law. The Senate must be adopted by a 2/3rds vote of the Senate and only then can the President ratify it by his signature. First the Senate must vote, then the President can sign it into law.
As part of his negotiation process he can sign the agreement, but it has no weight of law. For US legal purposes it's a symbolic gesture only as I understand it.
By custom the treaty would go to Foreign Relations then to the full Senate but I don't believe that's a requirement. It's a custom like the President submitting a budget. He's not required to do so.
Regardless nothing he agrees to has any force of law until the Senate votes it into law and he subsequently signs it, just like any law.
The only exception re international treaties, which is the loophole that worries me, is if something is brought into effect as part of an existing treaty or by some kind of bizarre legal accession. As a stand alone treaty I can't imagine what will come out of a committee where Iran is a respected member ever passing muster.
I wonder if this is to what he's referring, that there's some existing treaty framework out there that lets him claim this to be part of something to which the Senate already agreed. I don't know of any such thing and haven't seen it put that way in the media, but that's the best swag I've got.
I'll be surprised if Obama even endorses this thing. Too much of a risk for him before the election. He'd only validate the NRA's concerns and not really get anyone to vote for him that wasn't already going to do so.