Quoting from that source on the subject of "Citizens and natives":
VATTEL: THE LAW OF NATIONS
OF NATIONS CONSIDERED IN THEMSELVES.
OF OUR NATIVE COUNTRY, AND SEVERAL THINGS THAT RELATE TO IT.
§ 212. Citizens and natives.The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for, if he is born there of a foreigner, it will be only the place of his birth, and not his country.
So, the question must be asked: Is the original intent of the Framers of our Constitution still in effect? The Naturalization Act is not a formal Constitutional Amendment, though it is the law of record concerning the subject of citizenship.
The Founders would not have considered Obama a "natural-born citizen", therefore, today should we, or should we not? This seems like a conundrum only the Supreme Court can finally decide... and they have not, to date, ruled on it.
Oh, and as a further point, why is Obama's father's race listed as "African" on Obama's Birth Certificate? According to Vital Statistics Of The United States 1961 Volume I--Natality, Page 231:
Race and color
Births in the United States in 1961 are classified for vital statistics into white, Negro, American Indian, Chinese, Japanese, Aleut, Eskimo, Hawaiian and Part-Hawaiian (combined), and "other nonwhite." The category "white" includes, in addition to persons reported as "white," those reported as Mexican or Puerto Rican. With one exception, a reported mixture of Negro with any other race is included in the Negro group; other mixed parentage is classified according to the race of the nonwhite parent and mixtures of nonwhite races to the race of the father. The exception refers to a mixture of Hawaiian and any other race, which is classified as Part-Hawaiian. In most tables a less detailed classification of "white" and "nonwhite" is used.