In the US, it is plain and simple--soil counts. Where was the baby born? If you are on American soil, regardless of status, your baby is an American citizen. In fact, there have been numerous incidents around the border in San Diego of women in labor sprinting across the border, dodging traffic, and then collapsing on the US side to give birth.
You should note, however, that once the child is born in the US, you will probably need to follow up on the citizenship immediately, including issuing the baby a passport. I'm not certain on this, (ok?) but have heard a number of anecdotes and snippets of information of some parents who have not obtained a passport for their baby have, by default, renounced the baby's citizenship (or broken some US travel law), making the child ineligible for a US passport for at least 10 years. Actually, I think it was 10 years and no travel to the US.
Hmmm...You should read this:
http://britishexpats.com/forum/showthread.php?t=170029
It seems that US citizens, to travel abroad, need a US passport. So, if you take your US citizen child OUT of the US without a passport, they (you) will likely face a grilling the next time you try to take them into the US or try to obtain a US passport (as the 'child' has broken the law by being a US citizen and traveling without a US passport).
Like I said, there is a lot of FUD on this issue. Your best bet is to talk to the US consulate.