Who's job is it to make a determination as to what the term "natural born Citizen" means in the context of the Constitution?
I believe that would fall on the (fed) courts, not Congress. SCOTUS could within their power, make a determination as to whether someone born owing allegiance to a foreign power is considered a "natural born Citizen" as intended by the framers for AII,S1,C5 purposes.
In other words, they could find someone born with foreign allegiance owed to be eligible or not.
Congress certifies the election through a 'negative affirmation' process. Meaning if they do not assert and successfully challanged the election, then the election stands.
If they feel they made a mistake, they have a remedy, and that remedy doesn't entangle the U.S judicial system and SCOTUS into a political cat and dog fight. Oh, and that remedy is impeachment.
In other words, they could find someone born with foreign allegiance owed to be eligible or not.
USCON A1 S8 4th clause:
To establish an [SIC] uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
What is the difference between "Uniform Rule" and "Uniform Law"? Here apparently the USCON distinguishes between the two? I say a "rule" is something less than a law, but more than a procedure