Shunyata, According to the 14th Ammendment of the US Constitution, Babies born in USA will have an American Citizenship. The status of the parents won't be affected, meaning you still will be in student status. When your son/daughter is about 21 years of age, he/she can sponsor you for a Permanent Residence (GC) and subsiquently, a citizenship. So yes, if your visa expires and you don't get another status, you HAVE to leave the country. Legally, your child is not required to leave as he/she is a citizen.