That's not the point. By becoming president, he has a mandate, and, technically, the authority to enact that mandate, as long as it conforms with the strictures imposed by our laws and constitution.
But, if the president has any concern for our country, he wouldn't embark on a unilateral (domestically speaking) path. It is the role (I hope!) to be a representative for the interests of individual Americans, Americans as a whole, and, for the interests of the world at large (Kyoto agreement, International Criminal court, NATO, etc.), because that is where we live, in the world. There is no isolation anymore.