No, they don't. That's one of the more irresponsible pseudo-facts I've seen floating around here on FR. It sounds reasonable, and maybe it should be the law, but it's not the law. The law is staked out clearly in 8 USC 1401: Born in the U.S. That's it.
The law concerning BHO’s citizenship is not the current law, but the law in effect at his birth. That is the Immigration Act of 1952.
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Here is the U.S. Immigration Law that covers the issue of children born abroad to 1 citizen and 1 alien.
http://library.uwb.edu/guides/USimmigration/66%20stat%20163.pdf
the McCarran-Walter Act, the Immigration and Nationality Act of 1952
Public law 82-414 Chapter 1 Section 301 (7)
This applies to Obozo, assuming he is the son of Barrack H. Obama, Sr. and that he was born abroad.
If born abroad with the stated father, he is not even a U.S. Citizen.....
I see we have a new troll.
What are ya...nine?