This is true up and down the market. Here in New Zealand we've had a lot of squealing about "shortages in essential skills" from, I shit you not, cafe owners, bottle shop owners, you name it. We have restaurants who charge, I am not making this up, $300/head claiming that if they can't import cheap waiters paid $18/hour they'll go out of business.
The sad thing is that workers - and we see this in this very thread - end up attacking immigrant workers (who are merely trying to improve their lives), rather than employers who are exploiting workers on employer-tied work visas (both in terms of up-front pay, but often in terms of kickbacks and the like) to drive down local pay and conditions.
The answer would be that if there is a genuine labour shortage in local skills, the work permit should be in that industry/skill set, not employer tied. That would allow migrant workers to better their lot (and, given that many support extended family on remittences, whole communities) while allowing them to avoid being exploited by agencies or shitty employers; it would also avoid migrant labour being mis-used to depress local terms and conditions.
Unfortunately it seems easier to convince people to vote for anti-immigrant, often bigoted, political platforms than to convince workers to see their common interests.