The Senate does not get to approve the Iran deal, thanks to the Corker amendment. The Senate only get to disapprove the deal, then when O vetoes the disapproval the Senate must override the veto to kill the deal. Basically Corker approve the Iran deal with lots of face saving denials for Senators like Cruz bill into the deal. Just like TPA did for TPP.
You obviously don’t understand the Corker bill. Obama was going to seal the deal as an agreement, which a President has the authority to make. The Corker bill made it law that Congress (Not just the Senate) had to approve the Iran deal for it to be valid. We could argue all day about whether it was actually an agreement or a treaty, but the reality was Obama was negotiating it as an agreement. Without Congressional approval, according to law (the Corker bill) the next President can nullify the deal.
How is the Corker bill relevant to Cruz when we know he opposes the Iran deal and will repeal it as President?