Could be. I think the court process could be long and lengthy.
I have friends, legal ones, that got their US citizenship. They are still citizens of Mexico. They hold dual citizenship and can travel overseas with a US or Mexican passport.
Actually through much of the 20th century the US have deported mothers and babies back to their home countries.
It’s government policy or discretion, and it is a very low priority for the Obama administration to deport, especially families. There is no positive US law to compel government to prevent “birthright” citizenship.