Not according to the founders. When the founders passed the very first acts of congress, they included the naturalization act of 1790. But rather than speculating on their intent, lets let the founders speak for themselves by quoting from the act;
"the children of citizens of the United States that may be born beyond Sea, or out of the limits of the United States, shall be considered as natural born Citizens: provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States"
Now since we KNOW that Sen Cruz's dad did in fact, reside in the United States, and we KNOW that Sen Cruz was born a US citizen AND has never needed to be naturalized, we KNOW that he would have met the founders letter of the law as well as the spirit of the law.
You seem to think that residing and being a citizen is the same thing. At the time of Cruz birth his father was not an American citizen. Divided loyalties at birth, EXACTLY what the founders created the NBC to prevent.
Are you purposely ignoring that the act you are basing your statements on was repealed and cannot be used for any legal reasoning? In fact the way the Act was repealed not only negated your interpretation but proved the opposite.
Your own quote denies your position.
The father has to be a citizen AND a resident of the US. In other words, your father could be a US citizen, but never have lived here.