After reading the leaked draft, this is indeed the main line of reasoning presented: the argument from democracy. Highly contentious moral views ought to be decided by the people, this is one, therefore this ought to be decided by the people.
A second line of reasoning in the draft is an appeal to history or tradition. He argues that if a freestanding individual right to bodily autonomy is appealed to, well there's no historical basis for that, and after all it would lead to legalization of drugs and prostitution and that would just be crazy.