Even here on FR we have people who will fight tooth and nail for the children of foreigners to be President, precisely what the founders were trying to prevent.
The founders were smart.
If both immigrant parents were citizens at the time the child was born, it may be acceptable. The issue then would be foreign allegiance, which should be extinguished when they take the oath of loyalty when they gain citizenship. Some nations like England did at the time of the American Revolution, did not recognize our citizenship, they were conscripted often because they were English Subjects.
Children of Foreign born parents who are not citizens have no claim.
Note: here is where the article was posted on FR in 2009:
(Linkie no Workie)
Clearing the Smoke on Obama’s Eligibility: An Intelligence Investigator’s June 10 Report (7-28-09)
FR Comments: http://www.freerepublic.com/focus/news/2303258/posts