Most experts believe Cruz is a natural born citizen, but no president has ever been born outside the U.S.
My money is on one Barack Obama who was born in Vancouver, Canada to a mother too young to ever confer her USA citizenship onto the baby she was to give up for adoption but kept at the last minute, until she tired of him around age 5.
Somebody mentioned Chester A. Arthur, but I'm not familiar with his case.
In the case of Ted Cruz, there doesn't appear to be any "dual allegiance" issue, and that's one of the reasons I'm so confident that the USSC would unanimously determine Ted Cruz to be eligible for the office of President.
When one must pin one's hopes on a USSC which figures to be staunchly conservative, and rely on Justices like Clarence Thomas to be in a majority that would somehow rule Ted Cruz ineligible, this is simply not a realistic expectation.
To reiterate, I believe that virtually any USSC that you could arbitrarily construct would not consider Ted Cruz ineligible—and that either unanimously or near unanimously. Thus, whimsically hoping for some fantastical scenario where that wouldn't be the case is a purely academic exercise.
Politics is the art of the possible,ad—like it or not—the Supreme Court would rule within that realm—not the boundaries defined by wishful thinking and extreme idealism.
I'm open to any rational argument that could convince me that the Supreme Court—as currently constituted, or as likely to be constituted in the next couple of decades—would rule Ted Cruz ineligible, but I simply don't see a single Justice that I think would support such a ruling—not even a strict constructionist.