According Harvard, natural born citizen = citizen at birth. So if Cruz’s mother was a U.S. citizen when he was born, then according to that rule he is a natural born citizen. We haven’t yet seen proof that she was a U.S. citizen at the time of his birth.
http://www.cato.org/publications/commentary/yes-ted-cruz-can-be-president
The authors cite to the Naturalization Act of 1790 and ignore the fact that the Naturalization Act of 1795, with the lead of then-Rep. James Madison and with the approval of President George Washington, repealed it and specifically changed "shall be considered as natural born citizens" to "shall be considered as citizens of the United States."
James Madison the "father of the Constitution" changed the wording from "natural born citizen" to "citizen". Madison was no dope and the change was to prevent a foriegn born from becoming Commander in Chief. But this also serves to illustrate that "citizen at birth" does not mean "natural born citizen".
See more at
https://cdrkerchner.wordpress.com/tag/harvard-law-review/