No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.  -U.S. Constitution, Article II, Section 1

This seems pretty simple and reasonable.  We don’t want outside people running our country.  As was the purpose of the entire document, we want real people connected to the country to govern.  By this standard most professional politicians are ineligible. But sticking to the letter, in order to be President of the United States,  you have to be 35, have lived in the country 14 years and be a citizen by birth.  The second clause no longer applies, but was necessary because at the beginning no one was a citizen by birth, so the Constitution automatically qualified everyone.

It get’s a little more complicated because there are ways you can never claim or lose your citizenship.  Let’s say you were born in Kenya and your mother was a Communist, I mean American but she never files the appropriate paperwork, or you don’t spend enough time in the country before you are 18, your claim to citizenship is void.   It would allow you to go to college in America, for free, as an immigrant, but you can’t be President.  And if by some slight of hand, a big mafia hand from Chicago, you did become President, you would be the worst President ever.  Another option is that you could move to a country which doesn’t recognize dual citizenship, like say Indonesia.  If you want to be Indonesian, you must revoke your other allegiances.    Another scenario is if you say,  commit light treason, by I don’t know, stashing national security secrets in a bathroom in Colorado.  U.S. law states that you can no longer hold federal office.

But it’s a little absurd to suggest that going on vacation while you are pregnant puts your child’s citizenship in question.  Or how about men and women serving in the military in another country?  Would anyone suggest that you lose your eligibility?  What about going overseas for another reason?  Again the founders considered it; sure move away, as long as you live in the country for fourteen years before you run.

Further Reading:  http://www.nationalreview.com/article/429867/ted-cruz-natural-born-citizenship-eligibility-president