Is it your intuition that the labor market would not adjust to a lower supply by becoming more desirable? If not, why?
Research by George Borjas found that the influx of immigrants (both legal and illegal) from Mexico and Central America from 1980 to 2000 accounted for a 3.7% wage loss for American workers (4.5% for black Americans and 5% for Hispanic Americans). Borjas found that wage depression was greatest for workers without a high school diploma (a 7.4% reduction) because these workers face the most direct competition with immigrants, legal and illegal. [3]
Assuming ALL recent-ish immigrants are all mass deported and the economy adjusts immediately, you will see a ~7.4% shift of real wages for high school dropouts making the low end of <$36K, most of which voted for Clinton anyway. You'll see almost no issue with those above this rate because they are not competing with illegal immigrants. (This makes it more likely capitalists who see wage increases for non-service positions (eg manufacturing) will automate faster to reduce costs, but I think this is a side point considering that most jobs in the US today are in the service sector and not as easily automated away.)
Of course, you could also give the suppressed income bracket a 7% tax cut and end up in roughly the same spot without mass deportation; the undocumented immigrants aren't paying income tax anyway, and this would be HIGHER than necessary because the above study takes into account legal immigration as well.
[1] http://www.pewhispanic.org/2009/04/14/a-portrait-of-unauthor...
[2] http://www.npr.org/templates/story/story.php?storyId=5312900
[3] https://en.wikipedia.org/wiki/Economic_impact_of_illegal_imm...
[4] http://catalog.flatworldknowledge.com/bookhub/reader/2992?e=...
So, just excluding or including some more people won't change the level of pay, as a first order effect.
There's no constant demand for labour. It expands and shrinks with supply. (And even then, the federal reserve can make arbitrary large amouts of demand. They can literally print money.)
But where and when has there ever been this magical equilibrium?
In the real world people get paid whatever they can get away with, and some people can get away with more than others. Telecommunications execs can price gouge you and get a bonus for it.
This applies to the average Joe, too, by the nature of how averages work. (But might not apply to the median Joe.)
Yes, there's some pricing power for some people. And there's weird things like Baumol's cost disease. But those are second and higher order effects.
Exactly. And "we" after all is another abstraction. And "I" can eat what "you" sowed.
If corporations have record-high profits, while workers get stagnating salaries while housing prices raise, someone is going to realize what "we" entices after all.