Thank you for asking.
Justice Scalia suggests that in divining intent the focus the should be on what the term might have meant to "ordinary citizens" in the founding generation. In District of Columbia v. Heller (2008), the Supreme Court (J. Scalia) wrote the following:
"The Second Amendment provides: 'A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.' In interpreting this text, we are guided by the principle that '[t]he Constitution was written to be understood by the voters; its words and phrases were used in their normal and ordinary as distinguished from technical meaning.' United States v. Sprague, 282 U. S. 716, 731 (1931) ; see also Gibbons v. Ogden, 9 Wheat. 1, 188 (1824). Normal meaning may of course include an idiomatic meaning, but it excludes secret or technical meanings that would not have been known to ordinary citizens in the founding generation."
How many "ordinary citizens" then or now were familiar with Grotius or Vattel or the books they wrote in foreign languages? I recognize that there may have been a few of society's most elite back then who had such books somewhere in their libraries, but those aren't the kind of folks that I usually consider "ordinary citizens." "Ordinary citizens" back then or now aren't usually familiar with Vattel's theories on citizenship.
I think that if the term "natural born citizen" had in the minds of a few of the drafters some sort of special little meaning (in French or in English) and they wanted to bind Americans then or now to that special little meaning, then they were under an obligation to disclose that special little meaning in the text of the Constitution for "ordinary citizens" in the founding generation. I also think that, absent such a disclosure, "citizen at birth" seems to me a very normal, more natural, common-sense NBC construction for ordinary citizens (like me), then or now. If some now want to impose on the rest of us their special little meaning, then they should amend the Constitution and add the appropriate language.
The term Birther was to link people who thought Obama was born outside the country to 911 Truthers. Morons. Idiots. Insane. ...
People have told me that they are "birthers." Sure, many of them have discredited "birtherism" by their conduct, but the term isn't necessarily a pejorative as yet.
But, listen, give me an alternative term to describe them and I'll be happy to use it. I have no desire to offend you. ;-)
Justice Scalia explained his approach to interpreting the Constitution in his 1997 book - A Matter of Interpretation, Federal Courts and the Law
"It is curious that most of those who insist that the drafter’s intent gives meaning to a statute reject the drafter’s intent as the criteria for interpretation of the Constitution. I reject it for both. I will consult the writings of some men who happened to be delegates to the Constitutional Convention – Hamilton’s and Madison’s writings in The Federalist, for example. I do so, however, not because they were Framers and therefore their intent is authoritative and must be law; but rather because their writings, like those of other intelligent and informed people of the time, display how the text of the Constitution was originally understood. Thus I give equal weight to Jay’s pieces in The Federalist, and to Thomas Jefferson’s writings. Even though neither of them was a Framer. What I look for in the Constitution is precisely what I look for in a statute: the original meaning of the text, not what the original draftsmen intended.” ( 1997)