No, illegal immigrants are doing jobs that residents don't want to do (or can't do) at that price. They can afford to work for less because they're often working in order to send remittances, not to live a fulfilling, sustainable life, which is what they're hoping to do after they get back home.
> Businesses can't hire illegal immigrants on the books. They can't be waiters, retail workers, or other types of labor that the lower class depends on. So how does this impact America's poor and middle class? Absence of these workers should push prices higher.
Absence of those workers should push prices higher because it pushes labor costs higher - meaning that the effect you're noting here is evidence of the opposite of the claim you made immediately before. Absence of those workers should raise costs (which may or may not be reflected in prices), and also raise the salaries of people who work. Inflation is rising prices, rising wages, and falling debts.
Legalizing those workers and encouraging them to migrate their families here too would have the same effect, giving them the means to negotiate.
> H1B immigration [...] has never led to a decrease in the salaries of skilled workers. Software engineers have never made so much.
You're just making up the first part, and the second part is irrelevant to whether H1Bs lower salaries.
> More people working and living in the US will create more productivity and consumer demand, increasing the strength of our economy.
Lower wages = higher productivity. Lower wages != an increase in demand.
> Why all of the vilification?
Immigrants aren't the villains, the villains are these rationalizations for exploiting the precarious and brown for the sake of stockholders and owners. A quick an easy path to citizenship is just as objectionable to these people, because citizens have rights and can organize.