It becomes a matter of standing. I suppose the Dem nominee or another Rep candidate could challenge Cruz's edibility to hold the office. The fact that McCain asked to have it clarified by the Senate and that Tribe and Olson wrote their opinion on the matter is telling. Even in Senate Resolution 511, Congress admitted that the matter has not been resolved;
Whereas the term ‘‘natural born Citizen’’, as that term appears in Article II, Section 1, is not defined in the Constitution of the United States;