(This is probably your strongest argument.) This country was settled by people looking to exercise freely the religion of their choice. The First mandates government neutrality between religion and religion and religion and non-religion. The commandments tell us we are not to covet our neighbor's manservant or maidservant. The commandments remind us that they are from the Lord, our God, who brought the people ouf of Egypt, out of the land of slavery.
Why then, do people insist on government taking a hand in every grievance they have with their neighbor? And why do people insist that government address things better left alone? Why, in short, are people willing to allow government more control?
Congress shall make no law...prohibiting the free exercise thereof. You could perhaps argue that by banning homosexual marriage, the government is not interferring with the exercise of anyone's religion. You could not argue that an elected official could perform same-sex marriages under the canopy where commandments have been removed.
I'm not yet convinced that either a ban, or legalizing it, would be consistent with the 1st. The issue cannot be divorced from the issue of free exercise of religion.