Ok will add a few points here as I think some of this discussion is misleading. For more info, may want to search the EF, there was some discussion on this recently, and see the isaac Brock Society, they are heavily in to this type of issue at the moment,
http://isaacbrocksociety.ca . More info on citizenship at
www.aca.ch , american citizens abroad.
First, if both parents are US citizens, then the child, regardless where born is american. (jurus sangenis) Also through being born on US soil (jurus solis). However, these do not apply in the case of the OP as I understand, as only mother has US citizenship, and born here.
Second, if only one citizen parent, the possiblitiy to gain US citizenship is 'conditional' on proving some facts, ie. in the case of a mother, it has to be shown that she lived an uninterrupted stay, beleive it is one year if not married, and 3 if married, in the US during a certain age range. Same is true for only US citizen father, but different year thresholds apply and the out of wedlock child is different as well.
So what does this mean, it is clear that it if both parents american, child automatically american. For one parent citizen, it is not automatic and until one goes forward and claims and proves citizenship, the child cannot be claimed by american authorties as being american, unless the american authorities prove the conditional criteria. And for me, the last part would be difficult and or impossible for them to do, not to mention unheard of to go to such lengths.
For OP you are not alone in this situation, and many are in a similar situation, I would not worry too much about it and claimuse the citizenship she already holds.