I believe in US Code you only have to be born in the United States to be a natural citizen. If you qualify under that umbrella, question of parentage goes away...
The whole thing about a British father seems a bit like interpreting the constitution's 'loophole' for the founding fathers, since none of them were 'born' in the United States. The framers made a loophole that stated if you were a citizen of the United States at the time of ratification, then you would qualify to be president (as well as hold other citizenship rights). Otherwise Washington, Jefferson, Adams, etc. couldn't have been president because they were British citizens when they were born... the thing that mr Donofiro goes into about the founding fathers never meant for a child of a British father to be the president seems really odd...
However, I do believe that the first (and best) qualification for natural born citizen is to be born on US Soil. Obama certainly qualifies. The other points in the law are for special situations - mostly having to do with Native Americans and children of military parents.
Now, the subject to jurisdiction part may be up for grabs, I will make a phone call...
§ 1401. Nationals and citizens of United States at birth
(note - only one needs to be true to be a natural citizen of the United States)
The following shall be nationals and citizens of the United States at birth:
(a) a person born in the United States, and subject to the jurisdiction thereof;
(b) a person born in the United States to a member of an Indian, Eskimo, Aleutian, or other aboriginal tribe: Provided, That the granting of citizenship under this subsection shall not in any manner impair or otherwise affect the right of such person to tribal or other property;
(c) a person born outside of the United States and its outlying possessions of parents both of whom are citizens of the United States and one of whom has had a residence in the United States or one of its outlying possessions, prior to the birth of such person;
(d) a person born outside of the United States and its outlying possessions of parents one of whom is a citizen of the United States who has been physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the birth of such person, and the other of whom is a national, but not a citizen of the United States;
(e) a person born in an outlying possession of the United States of parents one of whom is a citizen of the United States who has been physically present in the United States or one of its outlying possessions for a continuous period of one year at any time prior to the birth of such person;
(f) a person of unknown parentage found in the United States while under the age of five years, until shown, prior to his attaining the age of twenty-one years, not to have been born in the United States;
(g) a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years: Provided, That any periods of honorable service in the Armed Forces of the United States, or periods of employment with the United States Government or with an international organization as that term is defined in section 288 of title 22 by such citizen parent, or any periods during which such citizen parent is physically present abroad as the dependent unmarried son or daughter and a member of the household of a person
(A) honorably serving with the Armed Forces of the United States, or
(B) employed by the United States Government or an international organization as defined in section 288 of title 22, may be included in order to satisfy the physical-presence requirement of this paragraph. This proviso shall be applicable to persons born on or after December 24, 1952, to the same extent as if it had become effective in its present form on that date; and
(h) a person born before noon (Eastern Standard Time) May 24, 1934, outside the limits and jurisdiction of the United States of an alien father and a mother who is a citizen of the United States who, prior to the birth of such person, had resided in the United States.
