The vast majority of Americans (pretty much everyone except Native Americans) are now or their families were immigrants. We seem to no longer value the "Melting Pot" theory in this country. Diversity and multiculturalism make us stronger, as does the desire for freedom and democracy. If an individual is a citizen of the US for a given amount of time (I have traditionally thought 20 years, but I kind of like Halx's idea of 35 years) and meets all of the requirements of serving as President, I see no reason why that one freedom should be withheld.
I am generally opposed to term-limits, as they infringe upon my constitutional right to vote for the person I want in office. I am, however, torn about the issue when it comes to the Presidency. I think it is fairly certain that Reagan would have gotten another term and the Clinton would have gotten at least one more, so it is a very real concern. Does anyone know if any of our past Presidents have commented on this?
BTW changing the natural born citizen stipulation has also been considered by the Dems, who would love to see Governor Jennifer Granholm:
http://www.michigan.gov/gov
have the opportunity to run for the the highest office in the land.