I think you have Cruz mixed up with the wrong committee. He was on the Senate Conservative Republicans Committee but it was not this group. Very confusing, but Ted was not on this committee. There are two with similar acronyms. Ted was not on this one.
Cruz was on both, but resigned the position on the NRSCC after the Mississippi mess. I just posted a link to an article about it. Sounds like Cruz pitched in to genuine conservatives, didn’t attend much of the NRSCC stuff, and set up the Senate Conservatives Fund to oppose the crap that the NRSCC was doing. Seems like he has since aligned himself with CONSERVATIVES and not necessarily REPUBLICANS, though the NRSCC work was to try to get a Republicn majority.