It should. But the Corker bill changes the rules. Treaties require the "advise and consent" of the Senate and 67 votes for ratification.
But the Corker bill tacitly accepts that the Iran agreement is not a treaty and, rather than 67 votes to ratify, requires 67 votes to override the President's decision.
Corker bungled the job.
At the risk of appearing dense, where is this "tacit acceptance" coming from? Spin should not count when it comes to matters like this. The language of the Constitution is clear. Isn't it at the very least worthy of an amendment to the bill when it comes to the floor? Force Obama to veto that.