Every conservative Senator (with the notable exception of Tom Cotton) including Senators Lee, Sessions, and Cruz ultimately voted for the Corker bill.
Senator Cruz’s reason for voting for it was that it would require President Obama to bring his agreement before congress rather than simply ignoring congress and doing it all at the UN which he was threatening to do.
Obviously a far better solution would have been for congress to simply impeach Obama if he didn’t present it for approval as a treaty. However, that was never going to happen with Boehner and McConnell as the Republican leadership. So, after their amendments were defeated and they were unable to prevent cloture from being reached, the conservative Senators ultimately decided to vote for it since it would at least delay Obama’s being able to get rid of the sanctions on Iran.