Don’t personalize it to Obama or anyone else...
Fundamentally, would having citizenship of another nation bestowed on you cause you to not be a natural born citizen?
Can I, a person born of two American citizen parents, born in Seattle, be eligible for the Presidency if Canada grants me citizenship?
As an adult, if you take an oath to a foreign nation, yes, you renounce your birth status for POTUS, however, if you reside in a foreign country and return to the US 14 years prior to running for office, you are still eligible.
A natural born citizen can only loose his/her status by a legal act during adulthood.
These hypotheticals of foreign nations somehow changing their laws to claim people whom have never stepped foot on their soil to be citizens is ludicrous. There is something called the ‘Law of Nation’, it does exist and ALL nations & sovereignties are bound by it to some extent. That is why treaties are made between countries such as the Expatriation Act of 1868 and other treaties between the US and other foreign nations regarding citizenship.
I would recommend you go to my site, click on the scribd link to Wilson & Story's commentaries and read them as well as get your hands on Edwin Meese’s Guide to the Constitution.