“...Do think Cruz is eligible to run for President under the Constitution?...”
His is not, nor did he need to be, a “naturalized” citizen. Hence, that leave only one citizenship class for him: Natural Citizen.
So with those readily available facts, how about you answer your own question: Is Cruz eligible to run for President under the US Constitution?
We really don't know. SCOTUS has yet to define what is meant by a "natural born citizen." We need that question resolved sooner rather than later. They had a opportunity to do that with Obama. The Senate commissioned Olsen and Tribe to come up with an opinion on McCain. You can read their decision here" They eventually issued a resolution saying McCain was eligible. If you read their conclusions, they include Obama and say he was natural born because he was born on US soil. McCain was born in Panama.
I have some problems with the Olson/Tribe conclusions, which support both jus sanguinis and jus solis as natural born citizens. One out of every 10 births in this country is to an illegal alien parent. Under US law, birthright citizenship, if you are born on US territory, you are automatically a citizen. Hence anyone born on US soil could run for President. Is that what the Founders meant?
I don't want to get too far into the legal weeds with you on this issue, but there was quite a controversy at the time over Chester Arthur's eligibility for the Presidency under the Constitution because his father was not an American citizen at the time he was born and that he was born in Canada.
I can see this issue coming to the fore the closer Cruz gets to the top of the pile. I wonder if the Reps in Congress will push for another legal opinion to have a similar resolution issued for Cruz.