Hawaii governor can't find Bork's birth certificate

I wonder what will happen if it turns out that obama was never an American ?

Obama is unquestionably American.

For most Americans, it is not hard to come up
with a birth certificate; its not usually a point of controversy.

And it wasn't hard for Obama to come up with a birth certificate either. His official birth certificate is available for everyone to look at online. It is the similar to any birth certificate any other American would get to show they were born in the US. The US government obviously accepted Obama's when he applied for a passport so any argument that it isn't valid is specious at best or plain old stupidity.

If the child of an American is born outside of America,
as a general rule, he is not an American.

Where did you say you studied law? Perhaps you have forgotten you should research the law before before you comment on it. At no time in US history has the child born to a US citizen not been an American as a general rule.

Congress first recognized the citizenship of children born to U.S. parents overseas on March 26, 1790, stating that "the children of citizens of the United States, that may be born beyond sea, or out of the limits of the United States, shall be considered as natural born citizens:

Copies thereof SHOUD BE AVAILABLE from the original issuing source.

If someone runs for the Presidency
who admittedly was born of an American citizen
who was on alien territory at the time of birth,
I 'm not sure whether he will be deemed a natural
born American citizen.

I doubt that Congress has the authority to change
what the Constitution says qua who are "natural born citizens."
Admittedly, there is a possibility that the Founders
did (secretly) embrace that definition in mind
that the children of American citizens born outside
of America will be American citizens. Maybe. I dunno.

If someone runs for the Presidency
who admittedly was born of an American citizen
who was on alien territory at the time of birth,
I 'm not sure whether he will be deemed a natural
born American citizen.

And again, you spout off without bothering to look into the complicated rules.

Under the majority of circumstances they would be deemed a natural born citizen of the US and eligible to be President. It is only under circumstances where their parents hadn't lived in the US for a decade or more that they would not have that status.

I doubt that Congress has the authority to change
what the Constitution says qua who are "natural born citizens."
Admittedly, there is a possibility that the Founders
did (secretly) embrace that definition in mind
that the children of American citizens born outside
of America will be American citizens. Maybe. I dunno.

For someone that doesn't know you sure seem
to have a strong opinion about who isn't able to be President.

It's not as complicated as you imply, Parados. In the Dred Scott case, the dissent (not contradicted by the majority) held that jus solis (place of birth) is the determinate, not descent by blood (jus sanguinis). This is the attitude taken in the fourteenth amendment, the very first sentence of which reads:

All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.

When reviewed against the text of Article II, Section One:

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; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States. (emphasis added)

. . . it is clear that any candidate for that office must be born on American soil (being naturalized doesn't qualify). Military installations, embassies and legations qualify as American soil, but simple descent does not make the cut. The Senator from Connecticut, Lowell P. Weicker, who came to prominence first from his participation on the Watergate Committee, was born of American parents in Paris. He was not eligible for the office, and it was discussed at the time, because he was a Republican and one of several names brought up to be a Republican standard bearer in that time of their disarray.

That Obama was born in Hawaii means that he is qualified for the offcie, even if both of his parents had not been Americans.

Professor Tribe agreed. Reading the “limits and jurisdiction” clause as Professor Chin does, Professor Tribe said, “is to attribute a crazy design to Congress” that “would create an irrational gap.”

There are, Professor Chin argued in his analysis, only two ways to become a natural-born citizen. One, specified in the Constitution, is to be born in the United States. The other way is to be covered by a law enacted by Congress at the time of one’s birth.

The following shall be nationals and citizens of the United States at birth:

You have also completely ignored what i pointed out,