The term "natural born subject" is clearly defined as a matter of English common law as being a person who is the subject of the sovereign of the place where he or she is born.
The term "natural born citizen" in our constitution was lifted by the framers from the English common law term and the word "subject" was changed to "citizen" because we don't have subjects (yet) but only citizens.
The more I look at the issue, the more I have become convinced that if I ever got the opportunity to talk to the U S Supreme Court on the topic, I think the meaning of the term in the U S Constitution is pretty clear.
We are not governed by English common law but by the Constitution and the laws made under it. But since you bring it up, the principle under English common law was that birth within the realm compelled loyalty to the King. As Justice Gray stated in the Ark case: "The fundamental principle of the common law with regard to English nationality was birth within the allegiance, also called "ligealty," "obedience," "faith," or "power" of the King. The principle embraced all persons born within the King's allegiance and subject to his protection. Such allegiance and protection were mutual -- as expressed in the maxim protectio trahit subjectionem, et subjectio protectionem -- and were not restricted to natural-born subjects and naturalized subjects, or to those who had taken an oath of allegiance, but were predicable of aliens in amity so long as they were within the kingdom. Children, born in England, of such aliens were therefore natural-born subjects. But the children, born within the realm, of foreign ambassadors, or the children of alien enemies, born during and within their hostile occupation of part of the King's dominions, were not natural-born subjects because not born within the allegiance, the obedience, or the power, or, as would be said at this day, within the jurisdiction, of the King."
So if you want to cling to English common law, then when you face the Supreme Court you'll have to say that if Obama was born in Hawaii as claimed then he's a natural-born U.S. citizen. Regardless of his father's nationality.