When we have the current Pope essentially calling deportation "...a crime against humanity"?
The Left enjoys media dominance. Not us!
I'm with you in theory, though! 
Stop giving out free shit, and start prosecuting for illegal entry, and you won't have to deport. The only reason these people are here is to collect free shit. But once they find out they get turned away from hospitals due to lack of funds or find that they can't enroll their kids in public schools because they are here illegally - once they get kicked out of their free apartment or hotel room and their SNAP cards get rejected, you will find them asking for transport to a country that still give out free shit. A country like Canada, perhaps.
This is a no brainer. And if the Pope doesn't like it, then we would be glad to sent them to Vatican City instead.
STOP HANDING OUT FREE SHIT TO PEOPLE WHOSE FIRST ACT ON AMERICAN SOIL WAS TO VIOLATE US IMMIGRATION LAW.