In a sense, is that already happening? The percentage of immigrants doing these service jobs must be quite high. Would that qualify as "going negative" since a portion of those salaries are going overseas and that "cheap" labor is being subsidized by government handouts?
On another note, I read A COUNTRY MADE BY WAR by Geoffrey Perret back in 1990. The hypothesis is that every war the US had been involved in has led to expansion and economic growth. Could the "IIC" (my own abbreviation, ask by private mail if your want to know what I'm saying) think that a war is just what the economy needs? If so, that would seem to be totally silly thinking as so many countries and small groups have the capability to annihilate things.
The jobs that can be exported are "information service" jobs. Service jobs with involve direct interaction with people, e.g. a nurse, or handling of materials, e.g. a waiter, do not fit. Nor do all jobs in the "service industries", e.g. an insurance salesman.
The information services jobs are ones which are essentially clerical in nature, such as sitting at a desk processing claims, providing help desk assistance to PC users in a company, an accounts payable clerk processing invoices in a manufacturing company and so forth. These jobs involve the flow of communications in and out of the position, the correlation of information, the consulatation of references, logical thinking, and other sedentary tasks.
I don't think these fit the types of jobs that immigrants currently perform, at least the low-paid, unskilled immigrants. These do the other types of hamburger-flipping services. This is not to say that there aren't a lot of highly paid H1B visa programmers and engineers around.
While outsourcing of IT work to the Far East is generating some objections, it is nothing compared with what will happen when the average department store shopper loses her desk job.