I'm not sure enough of what the issues are to present this as a poll, but how much do you care, and why? If possible, separate this issue from how you feel about Obama, McCain, and Schwarzenegger.
I can see the value of a rule of law, but I think the rule of law is blurrier than it sounds. There are laws that get ignored because people just stop bothering with them.
If you want to require "Americanness" of American presidents, it would seem more reasonable to require candidates to have spent some largish percentage of their lives (both childhood and adult) in the US, but if we can't even tell what "natural born citizen" means (no Caesarians?),
then an "enough time for the culture to rub off on a person" standard is impossible.