The new Senate make-up of power is 53 Democrats, 2 Independents (who will most likely caucus with the Democrats) and 45 Republicans. In order for a Treaty to be ratified by the Senate it requires a two thirds majority vote. Even if Obama signs on to this treaty that would mean both of the Indpedents, all of the Democrats and 12 Republicans would have to vote in favor of ratification. That ain't gonna happen. There are several Pro Second Amendment Democrats including Joe Manchin from West Virginia who would not vote for ratification.
If Obama tries to pull some kind of "End Run" around the Constitution it would be political suicide and any agenda he tries to promote for the remainder of his second term would be dead on arrival.