I can fly: In order to do that i.e. petition to remain in the U.S with a U.S born infant and be successful one has to prove "extreme hardship" to the infant if returned to the home country. I wish I could tell you what a successful application on grounds of "extreme hardship" constitutes but I doubt even the INS has a clue. A lot of these decisions are very arbitrary. You could try and show that the political scenario are horrible; that the education system as it stands will leave this U.S Citizen child at a disadvanatge when he/she returns to the U.S...but, the fact is that even these issues are likely going to be dismissed..you can certainly try and make the case but, please keep in mind that it likely going to take a while before you recieve favourable response.