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The constitution came before the Supreme Court. Correct.
And ....
Since the Constitution does not define the term, one must resort to (a) original intent; and/or (b) case law to define the term.

(A) ORIGINAL INTENT: As for "original intent," as outlined exhaustively in Lynch v. Clarke, the statutes and case law of all the colonies/new states at the time the Constitution was drafted provided that a child born in the colony/state was a citizen (natural born/native born), regardless of his or her parent's citizenship. Thus, as Lynch so eloquently states, if the Founding Fathers had meant to impose some new requirement and/or new definition, they surely would have provided for that in the Constitution. Given that they did not provide a new and different definition than that adopted in all 13 states, the only rational conclusion that can be drawn is that they meant to incorporate the existing meaning into the Constitution. And, to repeat: the "existing meaning" under the statutes and case law in all 13 colonies/states was that NBC=born in the colony/state.

(A) CASE LAW: With respect to case law, see links above.

Another quote from Lynch, which couldn't be any more direct.

Lynch v. Clarke, 3 N.Y.Leg.Obs. 236, 1 Sand. Ch. 583 (1844)
"Upon principle, therefore, I can entertain no doubt, but that by the law of the United States, every person born within the dominions and allegiance of the United States, whatever were the situation of his parents, is a natural born citizen."
"The entire silence of the constitution in regard to it, furnishes a strong confirmation, not only that the existing law of the states was entirely uniform, but that there was no intention to abrogate or change it. The term citizen, was used in the constitution as a word, the meaning of which was already established and well understood. And the constitution itself contains a direct recognition of the subsisting common law principle, in the section which defines the qualification of the President. "No person except a natural born citizen, or a citizen of the United States at the time of the adoption of this constitution, shall be eligible to the office of President," &c. The only standard which then existed, of a natural born citizen, was the rule of the common law, and no different standard has been adopted since. Suppose a person should be elected President who was native born, but of alien parents, could there be any reasonable doubt that he was eligible under the constitution ? I think not. The position would be decisive in his favor that by the rule of the common law, in force when the ' the colonies and in the states, under the constitution was adopted, he is a citizen."

LOL, dredging up Lynch v. Clarke & Lynch again, wherein the judge prefaces his remarks by saying he had no authority over the matter at all, under the Constiution, that his state, NY had no authority, and that only the Constitution can make any distinction. The Honorable Lewis H. Sandford declined to hand down any ruling, regarding natural born citizen status, because he did not possess the authority to do so. Go and read the opening paragraphs for yourself.

And, as to your earlier cite of Perkins v. Elg, Miss Marie Elg was born of two citizen parents under the law at that time, she was born in the United States, and therefore she was a natural born citizen. So, citing Elg is in no way helpful to you or to Obama.