I don't think anyone would argue that there is a shortage of service-sector labor. The debate there is purely over prices: there are business models designed around having large quantities of $7.50/hr-and-no-benefits labor available (in some cases, $5/hr under the table), and they are averse to having to pay more. But pretending that their unwillingness or inability to pay $10/hr means that there would be a "shortage" of unskilled labor at that price is disingenuous. There's plenty of it available, but maybe only for "fairly cheap" rather than "dirt cheap". That might just mean that certain business models are not very good business models.

In any case, that's not what the H1B program is officially about: the purpose of the program isn't supposed to be to keep wages down in sectors where wages would otherwise get too high for businesses to afford them. Instead the argument is that businesses literally can't find workers in these areas, so H1Bs constitute talent filling a critical national skills gap. My argument is that, if that were true, the wages in these critically-lacking sectors would rise accordingly.