If Cruz had voted against it we would still be here, and he would look pretty darn silly trying to use the requirements of a bill he voted against to stop the treaty.
This way Cruz did not undercut and eliminate or discredit his ability to push for stopping the bill on the basis of non-complience of the bill by the administration.
Sometimes what you are left with is your best strategy.
The bigger problem has become the lawlessness of the administration and the GOP cowardness on opposing it.
Cruz is on record as a signatory to THE legislation that got us here. When you cut through all the propaganda and theater that is the absolute nut of it.