Lindsay,

A more substantive reply to your points will have to wait a little while due to other work, and it may be worth a post of its own at my blog. For the time being, though:

Yes, coming into the US to work should be a more involved process than crossing a state line. At the very least, people who want to work in the US need to be issued Social Security Numbers or some functional alternative so that we can keep track of their payroll taxes and the legally-mandated contributions of their employers on their behalf.

I don’t think that anybody, whether native or immigrant, should be forced to contribute to Social Security in order to get a job. If they don’t intend to draw benefits that they didn’t pay in for, then it’s none of the government’s business. But if you think that it is necessary to issue new SSNs and subject immigrants to withholding taxes, then go ahead and issue those SSNs. But all that takes is one more sheet of paperwork to do at the point of employment, probably at the same time as the W-2. It has nothing in particular to do with imposing any kind of special restrictions or special ex ante screening for immigrants at the point of the border crossing, or as a condition for establishing long-term residency, and there’s no reason why enforcement should be considered a matter for immigration law, or punished by deportation, rather than merely considered a matter for tax law, as it would be considered if the person working off the books were an American citizen.

There’s no intrinsic connection between being an undocumented immigrant and working under the table. It is only because of the existing government restrictions on immigration, and the need to avoid government detection, that undocumented immigrants are disproportionately likely to work under the table.