Cruz is a much easier case (for challenging eligibility) than Obama was.
Again, I am not saying that any court will actually hold Cruz ineligible.
After all, we are living at a time when the power to regulate interstate commerce includes such things as the power to regulate growing your own wheat on your own property and making it into bread for yourself to eat, and the power to regulate your CO2 "emissions", and when the power to tax includes the power to force people to purchase specific health insurance contracts.
Only insofar as you have to accept more flawed premises. The premises that make Obama legitimate are also flawed.
The 14th amendment is nothing but a big statute, making it just another form of naturalization.