The Constitution clearly says Natural Born Citizen. All other references are to Citizens. So the original "intent" was for the president to be born of two citizen parents and that's EXACTLY what the constitution says. Now if you want to start arguing what the meaning of "is" is then you might falsely believe that Obama is eligible and slick willie did not actually have sex with that woman, Monica Lewinsky.
“The Constitution clearly says Natural Born Citizen. All other references are to Citizens. So the original ‘intent’ was for the president to be born of two citizen parents”
No, so far as we can know the president was meant to be a natural born citizen. Anything else is pure supposition, and does not control plain meaning. It could be useful for construing the text when it is unclear, but it’s not here. NBCs are people born citizens. That may have been only the children of two citizen parents at the original framing. By the 14th amendment, there is no doubt that it’s means more.