The media have demonized deportation to the point that many people think it's the equivalent of sending people to the death camps. Even so, there's no need for mass deportation. Just enforce the law. But even if we rounded them all up and bussed them out, it would be perfectly legitimate to do so.
I've asked this question a dozen times here and I've never gotten an answer from the open borders types. The question is: Do I have the right to enter any nation on earth anytime I feel like it, without regard to the laws of that nation? If I decide tomorrow that I want to live in Argentina, do I have a right to simply go there with no documentation, to sign up for benefits, to take a job from an Argentinian citizen? Would Argentina be violating my human rights if they booted me out?
The open borders people are afraid to answer that question. And the fact that they're afraid to answer it demonstrates what lying phonies they are.
Actually, there are tons of illegal Bolivians and Paraguayans in Argentina. The people are not too happy about it, but, much as is the case in the US, the government isn’t doing much to keep them out. Ditto the Nicaraguans in Costa Rica (over 20% of the population of Costa Rica was born in Nicaragua, and remember that Costa Rica has a very genrous welfare state).