While I do not think that Congress can change the definition of “natural born citizen,” I do believe that they can change the status of individuals so that they meet the definition. I don’t see any qualitative difference between legislation adding a new state to the union (and thereby making new US citizens at birth) and Congress making citizens at birth through legislation under their naturalization powers. No one would argue that only people born in the 13 original states can be President, so why should they argue that only people born under the English Common Law provisions governing citizenship in 1789 can be President?
I should point out that the Constitution does not define “natural born citizen.” One has to look elsewhere for the definition. For a definition, I look to the first Congress, who in 1790 by legislation made certain persons natural born citizens who were not natural born citizens before. Those Congressmen, one of whom, James Madison, is recognized as the principal author of the Constitution, decided that they could by legislation create natural born citizens, and the former President of the Constitutional Convention George Washington signed that bill into law. I do not think that the actions of the First Congress and President Washington are easily dismissed, nor are arguments of carelessness on their part credible.
The clear implication of the 1790 Act (and the Oxford English Dictionary) is that to our founders “natural born citizen” meant “citizen at birth.” So the question that remains is whether the Constitution’s naturalization provision gives Congress the power to create citizens at birth (in contrast to the usual understanding of naturalization–making someone a citizen after birth). The Congress has and does create citizens at birth (even in some cases retroactively) and I don’t know of any challenge to them doing that. (Judge Alsup in Robinson v. Bowen even opined that a retroactive act of Congress made John McCain a natural born citizen.) I see no objection to Congress changing membership in the pool of natural born citizens, through its naturalization powers.
If one were to invoke the English Common Law as both defining the term “natural born subject” and limiting which persons meet the definition, then I would point them to the various British acts that create natural born subjects, as argument against that position. That is, in 1789 Americans had a contemporary example of British legislation that expanded the pool of natural born subjects. Or put another way, I think that saying that English Common Law defines membership in the class of natural born subjects is the same mistake as saying that Minor v. Happersett defines membership in the class of natural born citizens–confusing necessary with sufficient conditions.)
Since according to U. S. Law, Canadian-born Ted Cruz was a U. S. citizen at birth, then yeah, he’s eligible to run for President.