After the first couple hundred thousand are booted out, the remainder will quickly get the message just as they did in the Eisenhower era and start packing. We can even sweeten the pot by providing transportation, box lunches and even small cash payments (payable at their nearest U.S. Consulate 90 days after they arrive home) for those who opt to waive their rights to a hearing. Start with, say, $1000 per person and ratchet it down as each quota is filled.
As for the old saw " . . . it would tear communities apart", the reality is that it would actually build communities in their countries of origin, reunite families and move people from overcrowded congested areas like Los Angeles to underdeveloped places like Mexico, which has roughly the same population density as Tennessee.
You're right in that removing millions of illegals would require a massive increase in the legal system that oversees it and changes to the laws. But nobody is talking about that. Trump makes it sound like it's as simple as snapping his fingers.