In the Venus Merchantman case of 1814, the SCOTUS, decided by members of the founding generation, lifted the entire 212th paragraph from Vattel’s Law of Nations to define Natural Born Citizen. Justice Livingstone quotes him as he wrote for the majority in that case. Vattel has been quoted in dozens of federal appellate decisions.
Your side will lose badly unless the court finds some sorta natural born citizen “penumbras and emanations” hiding between the pages of the constitution to support Cruz. (or Obama)
Most likely SCOTUS just refuses to hear the case. Too hot, and not a social justice thing that they are wont to push (like abortion and homo marriage). SCOTUS stood by silently as the circuit courts claimed the SCOTUS Presser case stood for the opposite of what it actually said. I can picture a scenario where the courts below find Bellei to stand for the proposition that Bellei is natural born. That's absurd to anybody who has read the Bellei case, but no more absurd than asserting that Presser stands for the proposition that states may intrude on the right to keep and bear arms.
In the evolution of Presser, this chronic and deliberate judicial dishonesty was not called out by SCOTUS, even though it was presented with multiple opportunities. SCOTUS is happy to let errors persist and even take firm root, as long as the outcome is the one they prefer.
The overwhelming majority of the powers that be, all of Congress, all of the courts, all of the players in the political parties, all of them see the NBC clause as an anachronism, and they will not apply it.
If SCOTUS rules that Bellei stands for the proposition that citizenship at birth, by statute, is natural born, that reversal has play in immigration law. The issue is not confined to presidential eligibility, although again I can imagine a court setting up a legal fiction where presidents-elect are natural born, but other people in the circumstance are not. That goes with the legal principle that laws apply to the little people, but not to the powerful.