This may sound really simple but regarding anchor babies and citizenship question, isn't there a simple solution?
If the mother is in the USA with a legitimate, legal justification and has proper paperwork, then yes a baby born on USA soil is a USA citizen. However if the mother somehow gained illegal entry into the USA and gave birth then the baby cannot be considered a USA citizen by birth, because the mother was only able to give birth on USA soil by breaking law(s) and illegally entering the USA.