The opposite of what you're talking about is commonly called inflation and that's not great either. As you rightly say, the key here is balance. I wouldn't know where to start on trying to decide where to draw the line on immigration - but I did read recently that an armistice on all current illegal workers in the UK, and the subsequent revenues raised on their incomes would create a net benefit of 6 billion pounds to the economy as opposed to cracking down and deporting them.
The other thing to point out about immigration (ignoring the legality of it for the moment) is that many of the jobs that immigrants take would simply not be filled by indigenous workers, normally because the pay would be too low, or the job itself deemed too menial.
On to some specific points of your post:
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The immigration-fueled reduction in wages does NOT help our economy. It hurts it. It reduces aggregate consumer income and the consumer spending it finances. The reduction in consumer spending reduces consumer production demand, further reducing demand for the labor to provide that production.
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Only if you are only counting domestic demand. If you include exports, then reduced wages tends to increase (external) consumer demand, bringing money into the country (in general).
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If that reduction is applied to the roughly 135 million employed Americans, that reduces aggregate annual worker income by $230 billion, or $0.23 trillion.
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Again, this point considers the country as a closed system. The problem with that is that considering wages/production/taxes etc within a closed system becomes meaningless. If everyone in a country earns 1.4% more, for doing the same thing, the actual effect is to devalue the currency by 1.4%. It's like trying to climb a rope that you're holding above your own head.
I'm surprised to hear that you consider pro-immigration (if that's what you're arguing against) as a right-wing ideal - My stereotypical ideas about "right-wingers" was that they were against immigration on largely xenophobic (cultural) grounds.
Anyway, on the whole I'd suggest that it's probably better to err on the non-inflationary side of the economic fence, since this way you are assured of a stable (if slightly boring) economy with none of the socially damaging boom and bust episodes that we've seen ravage communities since economics was invented.