Cruz’s position is not inconsistent at all. “Strict constitutionalist” doesn’t mean you can’t amend the Constitution. In fact that’s precisely what it means: if you want to change the Constitution, you have to amend it, not use “living document” BS to over-ride the plain language.

That having been said, this is theater. You probably couldn’t get 2/3 of Republicans to vote for a marriage amendment today. In the last poll, a good third of Republicans were in favor of same-sex marriage and opposition was waning.