[Beckwith]

Cannot an American woman pass her citizenship onto her bastard child?

Yes. In the same way the Kenyan father passed his Kenyan citizenship onto Obama.

Divided loyalties. Obama is a citizen, but not a "natural born citizen."

[MHGinTN]

In the case of Stanley Anne Dunham in 1961, no she could not pass citizenship to Barack or Barry or whatever his name of legal record is, because the law said then that she would have to live in the U.S. for five years past her fourteenth birthday, and the child was born when she was eighteen.