A critical insight that answers your previous question on how to do enforcement in an affordable manner. Start with the workplace.
Aside from the fact that E-Verify is simply
inaccurate (as well as my civil libertarian concerns related to a National ID card), mandating that employers subject every new hire to an
expensive and lengthy background check would increase labor costs significantly, which always has the effect of disemploying marginal workers - hurting the very low-skilled domestic workers you seek to help.
As for your claim that a liberalized immigration policy would lead to the unemployment and impoverishment of domestic workers who lack skills, if foreign workers are truly better at doing their jobs, it makes little sense to prevent them from doing so anymore than it makes sense to prohibit the use of labor-saving devices to ensure that manual laborers remain employed (not to mention it's fairly nativist to suggest that the economic wellbeing of domestic workers trumps that of foreign ones - not trying to accuse you of anything, just pointing out the logical implication of your argument). I'm not trying to dismiss the unemployment of poor natives as a non-issue, but surely there are better solutions for creating new jobs for them as opposed to imposing protectionist restrictions against immigrants who are simply better at doing their current jobs?