There may or may not be enough public support. Homosexual marriage was forced upon us by fiat. It was not common consensus nor vote.
Cite polls if you want but many can be cited and I no longer believe polls. In any direction.
The ceremony of marriage is a legal contract and there is nothing wrong with defining it exclusively.
But marriage licenses and homosexual activities are two different things. One is a government licensed activity - which the government can regulate - and the other is a behavior which the government can’t (under existing law) regulate.