In this very interesting poll, a majority of Americans say a child born outside the U.S. to one American citizen is not a "natural born" citizen. That percentage is likely to change, though:
The easiest prediction of the 2016 primaries is that Republicans will have a profound change of heart on who is and isn’t “natural born” once more of them become better acquainted with the circumstances of Ted Cruz’s birth.
[. . .]
The elephant in the room with all those numbers, though, is the Birther accusations that dogged Obama for the first few years of his presidency; lots of low-information voters have encountered the “natural born” question before only in the specific context of O’s birth, and as such, their views of it are infused with partisanship. Once the details of Cruz’s birth become more widely known, that partisan pressure will ease and the public will, I think, start to settle on the view that anyone born to at least one parent who’s an American citizen qualifies for the presidency, regardless of their place of birth.
That's sort of where I am on the issue -- you have at least one parent who is a citizen, you are a "natural born" citizen, no matter where you're born. That means the whole Birther thing was irrelevant for me, as is the birthplace of Cruz, or John McCain for that matter.
But who should and should not be considered natural-born is a complicated issue on which the Supreme Court has never really take a definitive stance.