According to Article 1, Section 8, para 4, Congress is authorized to establish uniforn rules of "naturalization." And they have done so. Foreigners and aliens who are not natural-born become citizens through the processes Congress has defined.
The Court in Minor established the meaning of "natural-born", setting precedent which Congress is not free to change. Here are the options (as explained by Donofrio) open for changing that understanding.
Check some of Newt Gingrich's writings, or those of other conservative writers, if you do not understand this point.
It is an EXTREMELY Liberal position to claim that only the Courts can make these determinations.
Next, in the case I spoke of, Madison clearly states that the CONGRESS has the power to determine who qualifies as a Citizen at Birth.
There are two types of Citizenship: Natural Born, or Naturalized. There are no other forms.