Of course it does.
Have you not read Federalist 68? Or Jay's letter to Washington?
Just where, in those conversations, did they believe it was okay for someone born with foreign citizenship, and foreign allegiance owed, to be eligibly for Commander in Chief?
Foreign influence in the government was a primary concern of the Framers, especially for the singular office of the Executive.
Framers were also concerned about “illiberality” in the admission of foreigners - they wanted to people the land.
Separating the qualifications for citizenship from the qualifications for office was the solution.
After months of discussion the qualifications for the Executive were at an impasse, no qualification seemed secure from foreign influence, until Jay’s “strong check” suggestion that the Executive “shall not be given to nor devolve on, any but a natural born Citizen.”
“Natural born citizenship” is not a source of citizenship, it is a quality of citizenship required for an office of government: the Presidency.
Here in the 21st century, sixteen court decisions have ruled Barack Obama to be a natural born citizen and he published a book about his Kenyan born father 13 years before he ran for president. No court decision and no act of Congress has found him not to qualify. I predict that it will be the same with Senator Cruz.
Allen v. Obama, Arizona (2012)
Ankeny v. Daniels, Indiana (2009)
Fair v. Obama, Maryland (2012)
Farrar v. Obama, Georgia (2012)
Freeman v. Obama, Illinois (2012)
Galasso v. Obama, New Jersey (2012)
Jackson v. Obama, Illinois (2012)
Paige v. Obama, Vermont (2012)
Powell v. Obama, Georgia (2012)
Purpura, et. al. v. Obama, New Jersey (2012)
Strunk v. N.Y. Board of Elections, New York (2012)
Swensson v. Obama, Georgia (2012)
Taitz v. Obama (Quo Warranto), Washington, D.D. (2010)
Tisdale v. Obama, Virginia (2012)
Voeltz v. Obama, Florida (2012)
Welden v. Obama, Georgia (2012)