If strong minority want it, it will happen in the same mode.
You've alluded to what I think most conservatives here don't get about this debate. They look around them, and they see only heterosexuals (they think) in their town, their workplace, their neighborhood, or their church. It's easy to get caught up in thinking that the rest of the world is pretty much like the people you know.
Out there in the cities, or in suburbia, a lot of people, liberal, conservative, and mushy middle, know gay people. Sure, they've seen the swishy drag queens, but they also know Henry down in accounting, who wonders whether the boss will freak if he brings a "guest" to the company picnic. They know they've never faced a problem bring their opposite sex spouses and dates to the picnic, so they feel a twinge of understanding with Henry.
Now, many of those people would not come to Henry's wedding, and might very well feel uncomfortable if Henry invited them, but if Henry wants to do this someday, they have a problem with amending the Constitution so that it can never happen. They know that someday, a lot of people are going to know a Henry, and it won't be such a big deal. So while they know that a lot of their friends, neighbors, and family are not ready for Henry, someday it might not be the case, and they really don't want an FMA to have to take down.
Besides, even if Henry makes them uncomfortable, the whole Amendment thing seems a bit mean spirited.