It certainly would be accepted better if it was done by popular vote. I think much of the opposition to same sex marriage isn't against it per se, but it is a backlash against making it legal by judicial fiat.Same sex marriage is like abortion or women combat troops in the front lines. Same sex marriage is like gender apartheid marriage where before marriage had perfect gender diversity, integration and union.
Judges should rule by law, not wright law. Sympathy isn't the function of justice, maybe they should go to church, where they encourage charity and mercy. Law is for consistent results along tradition and precedent, not radical new standards of marriage.
I think if a popular vote were held today, it would probably pass. And avoid much backlash against it.