According to this essay, we were never meant to have birthright citizenship.  It fell under the jurisdiction:

Thus, two requirements were set for United States citizenship: born or naturalized in the United States and subject to its jurisdiction.

By itself, birth within the territorial limits of the United States, as the case of the Indians indicated, did not make one automatically “subject to the jurisdiction” of the United States. And “jurisdiction” did not mean simply subject to the laws of the United States or subject to the jurisdiction of its courts. Rather, “jurisdiction” meant exclusive “allegiance” to the United States. Not all who were subject to the laws owed allegiance to the United States. As Senator Howard remarked, the requirement of “jurisdiction,” understood in the sense of “allegiance,” “will not, of course, include persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States.”