No, he does not.
Author of the 14th Amendment John Bingham defined Natural Born Citizen unchallenged. That definition is Born under the sole jurisdiction of... Obama was born under two, he could never even for an instant have been a Natural Born Citizen regardless of where he was born.
John Bingham was from Ohio, and absolutely an Abolitionist. His definition went into them congressional record, and NO ONE ever challenged his specific definition of NBC.
"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 constitution was adopted, he is a citizen." -- Lynch v. Clarke, 3 N.Y. Leg. Obs. 236, 1 Sand. Ch. 583 (1844).
"Nothing is better settled at the common law than the doctrine that the children even of aliens born in a country while the parents are resident there under the protection of the government and owing a temporary allegiance thereto are subjects by birth." -- Inglis v. Trustees of Sailor's Snug Harbor, 28 U.S. 99 (1830) (Storey, J.)
"We start from the premise that the rights of citizenship of the native-born and of the naturalized person are of the same dignity and are coextensive. The only difference drawn by the Constitution is that only the 'natural born' citizen is eligible to be President." -- Schneider v. Rusk, 377 U.S. 163 (1964).
"The first section of the second article of the Constitution uses the language "a natural-born citizen". It thus assumes that citizenship may be acquired by birth. Undoubtedly, this language of the Constitution was used in reference to that principle of public law, well understood in the history of this country at the time of the adoption of the Constitution, which referred Citizenship to the place of birth. At the Declaration of Independence, and ever since, the received general doctrine has been, in conformity with the common law, that free persons born within either of the colonies, were the subjects of the King; that by the Declaration of independence, and the consequent acquisition of sovereignty by the several States, all such persons ceased to be subjects, and became citizens of the several States" -- Dred Scott v. Sandford, 60 U.S. 393 (1857) (Curtis, J., dissenting).