I would be interested to hear any historical examples at all of problems to which a "grassroots right wing movement" was or should have been the best answer.
The "problem" (such as it is: millions of people coming in to work in the service sector at extremely low wages is a problem for US workers, but not for US businesses or US consumers) is surely the demand of American employers for- and their ability to get- extremely cheap below-the-board labour.
Therefore the solution is a simple and logical one: an enforceable minimum wage that can provide a living standard for US citizens, and (shock horror) representative mechanisms in the workplace (i.e. unions or other employee associations) that can enforce these standards on a thorough and daily basis. Thus: a rational meritocracy! No labour arbitrage by employers bringing in people who can be forced to work cheaper because of their shady situation. Everybody is judged on their ability to do the job. And everybody who does the job pays taxes and in return is genuinely entitled to use government services.
I mean, perhaps this sounds optimistic- but would bet my Celtic Frost albums that if when you look at the workplaces where there is the most exploitation of undocumented migrants in the worst conditions, they are also the workplaces where labour strength is lowest.