Does the Vice President need to be a "Natural Born Citizen"?

Or how about anybody else in line of succession? If, say, Ted Cruz was President Pro Tem of the Senate, something like fourth in line, would his citizenship matter? How about Nikki Haley, who appears to be a strong Republican Veep contender but is an "anchor baby"? Or for a more extreme example, what if Trump decides to have Arnold Schwartzenegger for Veep?

via International Skeptics Forum http://ift.tt/1ow01fx