After more thought, I see the play this is getting in the press as an example of them buying their own biased and stereotypical Leftist propaganda.
Remember that the Left believes that Conservatives are homophobically obsessed about gay marriage. Cruz saying this plays into that stereotype and bias: OF COURSE it’s going to hurt Cruz, because denying homosexuals marriage equality is a core component, THE core component, of what makes one a “Conservative”.
(I’ll add an aside here that it’s also projection, since it’s the Left thats really obsessed with the identity politics of race, gender, class, orientation, etc)
The Left doesn’t “get” that Conservativism is rooted in a deep believe in the Constitution and Bill of Rights and commitment to the founding ideals of this nation. In part because of their own obsession with “identity” but also because they don’t see the Constitution as an absolute but rather political silly putty that can be twisted and shaped to fit their needs.