No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution,
The second half of that was put in to give the founding generation and those alive and currently citizens, people like Jefferson, eligibility for the office. Once the generation passed you had to be a natural born citizen. So, what was the definition of natural born citizen? We can look at English Common Law and specifically at Blackstone's Commentaries which was one of two universal guides to English Common Law. In his commentary it is very clearly defined that paternity (Jus sanguinis) is the sole guide to determining allegiance. Something the US adopted.
"Yet the children of the king's embassadors born abroad were always held to be natural subjects: for as the father, though in a foreign country, owes not even a local allegiance to the prince to whom he is sent; so, with regard to the son also, he was held (by a kind of postliminium) to be born under the king of England's allegiance, represented by his father, the embassador."
The Law of Nations by Vattel also echoed both Jus soli and Jus sanguinis in defining a natural born citizen as "those born in the country, of parents who are citizens. Obviously the definition has evolved over time.
In short, if you are going to accept the new definition and progressive living breathing document theory as your justification for Obama being eligible you must do the same for Cruz and Rubio. You can't take an originalist view in one instance and not the other, nor can you adjust the definition yourself to meet your world view. This also applies to conservatives who claim Obama was not eligible because he does not meet original intent. You cannot accept that Cruz and Rubio are eligible while simultaneously stating Obama is not.