History proves that illegals will self-deport if there is a national program, like Operation Wetback in the 50's, to solve the problem:
Then on June 17, 1954, what was called "Operation Wetback" began. Because political resistance was lower in California and Arizona, the roundup of aliens began there. Some 750 agents swept northward through agricultural areas with a goal of 1,000 apprehensions a day. By the end of July, over 50,000 aliens were caught in the two states. Another 488,000, fearing arrest, had fled the country.
By mid-July, the crackdown extended northward into Utah, Nevada, and Idaho, and eastward to Texas.
By September, 80,000 had been taken into custody in Texas, and an estimated 500,000 to 700,000 illegals had left the Lone Star State voluntarily.
Unlike today, Mexicans caught in the roundup were not simply released at the border, where they could easily reenter the US. To discourage their return, Swing arranged for buses and trains to take many aliens deep within Mexico before being set free.
Tens of thousands more were put aboard two hired ships, the Emancipation and the Mercurio. The ships ferried the aliens from Port Isabel, Texas, to Vera Cruz, Mexico, more than 500 miles south.
I have some doubts that the gov't would commit the resources for the 1.2 million apprehensions, or that current legal procedures would allow their removal to go as smoothly as in 1954.
I do think that most of the enthusiastic "self-deport" believers are claiming that just employer enforcement, or aprehensions of a lot less than 1 million, will do the trick. I could be wrong, but I don't think Ii have seen anyone who is a promoter of "self-deport will solve the problem" arguing that "self-deport" means 1 million + apprehensions.