Well, it’s not like there isn’t precedent, courtesy of Senators Corker and Cruz and 97 others.
A presidential agreement can be unbound by another president. Only a constitutional treaty is binding as the law of the land.
The senate has time and again neglected to check Obama’s abuses. Of course, this just invites him to grab for more and more power and to bypass them with no consequences.
The senate has failed to perform its responsibilities under the Constitution. They all need to get the boot.