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In 1980 Jimmy Carter agreed to accept Cuba's political prisoners. Castro emptied his jails and mental asylums. If they are allowed in, there is no guarantee that they can be returned. Mexico said they would not take them. The non-Mexicans cannot just be returned to Mexico, even if they entered via Mexico. I doubt their home countries want them back. A lot of them will make money here and send it back there. Should they make a baby here, the child would be a natural born U.S. citizen and could not possibly be deported to a foreign country.

The future of this is probably like Bill Clinton's modest middle class tax cut. That was a campaign promise. Addressing the nation as President, he bit his lip and said he tried, he never tried so hard to do something, but he just can't. And that was the end of the modest middle class tax cut that was never going to happen.

The most realistic scenario if the government became determined to get rid of as many as possible would be self-deportation, i.e. they just leave on their own. They could be encouraged to do that by cutting off all benefits, especially work permits and anything the government pays for. The government always has ways to make people miserable.