I was ten or thereabouts when the Court handed down its opinion in Brown v. Board of Education. I remember the uproar in the South. One southern governor said he was trying to raise another Confederate Army. The governor of Texas threatened to call out the Texas Rangers (whoopee). The south was solid Jim Crow and the rest of the country was almost as segregated de facto. But the Court didn't hesitate in striking down "separate but equal" or in pointing out that separate is inherently unequal. They didn't take a poll; they didn't worry about the voters taking out their fury at the ballot box. They ruled as they believed the Constitution obligated them to rule. It was not popular and a few years later, they had to come back with the "all deliberate speed" decision - more emphasis on deliberate than speed.
Protecting the rights of minorities against the tyranny of the majority is never popular and it is never easy, but the plain English of our Fourteenth Amendment and the deepest traditions and ideals of our political system demand that it should be done.
A lot of people, perhaps most people, will object violently if the Supreme Court upholds the right of GLBT Americans to marry the person they love. It's not going to be easy. But it's equal protection of the law and that's what the Fourteenth Amendment requires.