“Yet, under current laws, illegal immigrants can sneak across the border and give birth and her child WOULD be eligible to run for president.”
No, that is a false statement. The illegal immigrants are foreign citizens, so their child is also a foreign citizen at birth with all of the obligations for obedience due to the foreign sovereign and the foreign sovereign’s laws, whether or not the child chooses to adopt that foreign citizenship upon reaching the age of majority. The same is true when the father is a U.S. citizen and the mother is a foreign citizen. In both cases the fact that the child was a U.S. citizen at birth due to the authority of a manmade and unnatural law granting such citizenship does nothing to change the fact the child was born with an allegiance and attendant allegiance and legal obligations to a foreign sovereign and foreign laws.
The natural born citizen clause was written to deny the Office of the President and the Office of the Vice President to any person who at anytime from birth to election was ever subject to the obligations of allegiance and obedience to a foreign sovereign and the laws of a foreign sovereign, with the exception of the Founders and their generation. This safeguard was intended to prevent a foreign sovereign from using the foreign sovereign’s legal authority to command a future U.S. President or Vice President or otherwise influence them to respect their obligations of obedience to the citizens of the United States and the Constitution.
The example you used results in a child who acquired U.S. citizenship only by the authority of a Federal statute or Federal law granting such U.S. citizenship at birth; which is a manmade, artificial, and unnatural law and unnatural citizenship by naturalization at birth. Natural born citizenship is acquired only by descent from two parents who were U.S. citizens at the time of the child’s birth, and none of the parents or the child were subject to a foreign citizen’s duty of allegiance and obedience to a foreign sovereign and a foreign sovereign’s laws. So, the child in your example was not a natural born citizen and can never be eligible under the natural born citizen clause of the Constitution.
Its ironic then that “The Father of the Constitution” James Madison accepted French Citizenship and could have voted in French elections.
“The Writings of James Madison 1790-1802”
https://books.google.com/books?id=BX3GAAAAMAAJ&pg=PA125&lpg=PA125&dq=james+madison+accepts+french+citizenship&source=bl&ots=iCEOOI-eaD&sig=-DelpRxq32kvrgBKeyeCTgNfN8I&hl=en&sa=X&ei=uNUQVbm-JMbpoASxsIGABg&ved=0CBIQ6AEwAg%23v=onepage&q=james%20madison%20accepts%20french%20citizenship&f=false/#v=snippet&q=james%20madison%20accepts%20french%20citizenship&f=false
You completely missed my point. That’s OK, I’ve decided to ignore the new Birthers.