McCain just didn't think the constitution was the vehicle for opposing gay marriage--a lot of conservatives have taken that position. I think he has a point. The constitution has never been used to deny rights or privileges. I'm not comfortable with doing it now though I oppose gay marriage. It should be left to the states to decide--isn't that the conservative position? And so far nearly all the states have gotten it right. But McCain has made clear he opposes gay marriage. He's stated it over and over. He's also remaining steadfast in opposing gays in the military.
Amending my prior post re: my comment about the constitution never having been used to deny rights or privileges, I should say of course that prohibition was in the constitution denying the ability to use alcohol. But we saw how well that worked out and most agree now the constitution was the wrong vehicle for enforcing temperance.
You should also read the Constitution. It has been used to restrict an individual’s right to their income and to drink alcoholic beverages.