If the kid is a citizen, I welcome him to live in our country for his/her whole life.
The parents, if they are here illegally, have to go.
I would favor giving the kid a free passport, allowing them to return when they can.
That's what's at the heart of the issue. Children born on US soil to illegal aliens should not be automatically granted US citizenship.
They should be sent back to their home country with their parents, until such time that they work their way through our legal immigration system - if they even desire to do so. They may not.