In terms of reducing unauthorized immigration, it would be much more effective and much less intrusive than ICE checks of people wherever they may be to (a) have all employers use E-Verify, and (b) have more allowed immigration. But (a) has opposition from both the left and the right (for often different reasons), and (b) is opposed by the same people who complain about unauthorized immigration, since they mostly want to reduce all immigration (sometimes for racist purposes, like FAIR and CIS founder John Tanton’s statement that he had “come to the point of view that for European-American society and culture to persist requires a European-American majority, and a clear one at that” http://www.detroitnews.com/story/news/michigan/2017/03/15/mich-man-led-immigration-fight-nearly-forgotten/99193990/ ).