That is indeed the crux of the issue. The latest immigrant bashing (that's essentially what anti-"illegal immigration" sentiment comes down to) is the result of high unemployment rate. What is a job? Why do we go to a job? We go to jobs in order to get paid! Anyone disagree with that is welcome to come work for me for free. There is always more work to be done; the lack of funds to pay for them is what prevents jobs from taking place. That means, "jobs" belong to the consumer and the employer, not the employee! i.e. work to be done and more importantly willingness to pay. Jobs do not belong to the employee, anymore than consumer's or the employer's money belongs to the employee or contract supplier who is not willing to stay competitive. Most of us here can understand this point quite clearly in the context of UAW workers fantasizing about their jobs belonging to themselves instead of belong to viable carmakers and ultimately consumers willing to pay up for the cars. Many seem to lose sight of this when "the union" membership is issued by the government (citizenship, or whatever paper "legality") instead of even a nominally voluntary organization like a labor union in the context of a closed shop.
Once we understand that jobs belong to the consumers and by extension employers who are willing to pay, then it is easy to understand that anyone who is able and willing to deliver the same goods or service for less cost indeed create jobs: so that consumers (and by extension employers/entreprenuers serving the ultimate consumer demand) have money left over to hire someone else to have additional work done (i.e. new jobs). This is the same reason why mechanisation/automation create jobs for the economy and improve the overall living standards even as they eliminate jobs in the specific sector that is being mechanized/automated. Failure to understand this led to the Luddite Movement, which took the form of ripping up railroad tracks in the mid-19th century as a way of protecting horse carriage jobs. I suppose if we outlawed internet, there could be many more courier jobs recreated, but is that really what we want?
That's before we even consider the cost of enforcement. Government enforcement against "illegal immigration"/"illegal employment" is essentially a "negative bridge" or "negative railroad," one that instead of facilitate commerce puts barriers and roadblocks in commerce. That will indeed destroy real productive jobs, not just that of the "illegals" but also American citizens due to compliance cost. All the new bureaucrats will have to be paid by American taxpayers. Even after all the "illegals" are tossed out, the new crop of bureaucrats will be looking for new ways to justify their own existence on taxpayer payroll, probably hassling American citizens in new ways as more and more categories are proscribed as "illegal" (the concept of "illegal immigrant" simply did not exist before the late 19th century union movement). Chances are though, all the "illegals" will never be thrown out entirely. The entire exercise would be like the "War on Drugs," only many times worse, as people have legs and can move themselves, unlike inanimate narcotics.
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