[Jameison]

"Going after 20 million illegal aliens will take a massive effort unparalleled in this country"

True.
But no one is suggesting it can all be done today, in one fell swoop. But it can be done.
We did the Normandy landings, built the Panama Canal, after the French had given up, put a man on she moon, etc.
They all took massive unparalleled efforts.

But more importantly that 12 million is a straw man's argument, as Thomas Sowell put it so succinctly here:

"Yet another insult to our intelligence is saying that, since we cannot find and deport 12 million people, the only choice left is to find some way to make them legal. There is probably no category of law-breakers -- from counterfeiters to burglars or from jay-walkers to murderers -- who can all be found and arrested. But no one suggests that we must therefore make what they have done legal. Such an argument would suggest that there is nothing in between 100 percent effective law enforcement and zero percent effective law enforcement.
The reverse twist on this argument is that suddenly taking 12 million people out of the labor force would disrupt the economy. No one has ever said -- or probably even dreamed -- that we could suddenly find all 12 million illegal immigrants at once and send them all home immediately. This is another straw man argument. The real question is what we do with whatever illegal aliens we do find. Right now, there are various communities around the country where local officials have a policy of forbidding the police from reporting illegal immigrants to federal authorities."

[MACVSOG68]

But more importantly that 12 million is a straw man's argument, as Thomas Sowell put it so succinctly here:
"Yet another insult to our intelligence is saying that, since we cannot find and deport 12 million people, the only choice left is to find some way to make them legal.

Two points, First it is not 12 million, but closer to 20 million. Second, as much as I like Thomas Sowell, there are several good reasons, not simply because we would never be able to round up 20 million assimilated immigrants. First, it would take a police state effort and Americans simply don't want that. Second, it will be akin to body count in Vietnam. We will go after the low hanging fruit first, meaning those who are actually here working with families, not the drug runners, gang members and others engaging in illegal operations. Third, without a carrot and stick approach, we will simply drive more of them underground, since they effectively have nothing to go home to. Fourth, the churches will provide safe haven should we make any kind of a large scale effort at catching and deporting. Fifth, the court system will have to be enlarged dramatically to handle 20 million cases even over 20 to 30 years. Sixth, many communities will simply refuse to cooperate with this effort. Thunderstorm. More later.