It is said that the influx of immigrants, especially illegal immigrants, has put downward pressure on wages at the low end of the spectrum. We hear horror stories of Americans, who typically won't work for less than the minimum wage, being laid off and replaced by illegal Mexican immigrants who will.
I can't question the veracity of these reports, since at least some of them are backed up by serious research. However, another question needs to be addressed, which is: why do Americans need a certain wage level?
It is at this point that the question of this country's extreme levels of economic inequality enter the picture. Those at the very top, who are receiving a vastly disproportionate share of nation's total income, are able to casually bid up the prices of almost everything, most especially those goods and services which are high in labor content (education, health care, etc.). If the rich can easily pay extraordinary amounts for tuition at selective universities like Harvard or Stanford, these universities will go ahead and charge those amounts, thereby making these schools largely unaffordable for those who have the academic credentials but not the money. And in fact we have seen tuition at these (and many other) schools drift steadily upward to the point where only the wealthiest parents can afford them. Recent studies have shown that, at selective schools like Harvard, the percentage of students coming from the highest income percentiles has been growing steadily.
In the case of health care, the rich don't need insurance, and don't care about it, which first of all deprives the insurance pool of their direct contributions, and which secondly ensures that the rich will oppose politically any attempt to institute a national single-payer system, a system which they probably won't be able to avoid contributing to, even though they have no intention of using it. As we know, legislators in Congress are far more likely to do the bidding of the wealthy than of the non-wealthy (even if blatant quid-pro-quo situations are fairly rare).
So, the non-rich need a certain level of income simply in order to buy ordinary necessities, the prices of which are out of sight compared to those found in countries with less inequality and better systems of public provision.