Can they? Are the American-born children lawful citizens of the countries the parents are being deported to?
That's their problem, not America's.
Of course. The US is the only country that offers birthright citizenship. If a Mexican couple had a child in the UK, that child would not be a British citizen. Would that child be without citizenship to any country? Of course not...they would be citizens of the parent's country.
The media always forgets to mention that...
I did see an article recently where it said that lots of illegals in the US are visiting the Mexican consulates to get Mexican passports for their US born children. A very good sign.