If he runs I'd bet, if they take the case at all, the courts (ultimately the Supreme Court if necessary) will rule Cruz eligible.
I am sincerely doubtful that the U.S. Supreme Court would rule Cruz eligible. They do not like over ruling a former Supreme court’s holding. See my post at #133.
The following is often used to support Marco Rubio, but the facts disputing the supporting argument can also be applies to Ted Cruz:
“The First U.S. Congress included in the 1790 Immigration & Naturalization Act language to alert the State Department to the fact that Americans born abroad are “natural born citizens” and are not to be viewed as foreigners due to foreign birth. They were not granted citizenship via that US statute rather their automatic citizenship was stated as a fact that must be recognized by immigration authorities. They were not citizens by any other means than natural law, and statutory law was written to insure that their natural citizenship was recognized.”
This is not a reasonable explanation. It fails to recognize that Congress only has powers over naturalization. Congress has no power to define “natural born Citizen”, which has nothing to do with naturalization. Furthermore, if Congress wants to tell the State Department something, they don’t have to enact legislation to do it.
But more important is that all of the following naturalization acts, 1795, 1802, etc., were also passed to naturalize the children of U.S. citizens born abroad. And the words “natural born” were repealed in the 1795 Naturalization Act and never returned again.
I'd be willing to take that bet as well.