Easy as pie.
The basic generalities of economics were developed in the time of Say and Smith. To whatever extent that they were valid then, they were in the context where a large company might have a dozen employees, barriers to entry were not huge, and there was no great opportunity for monopoly.
Contrast today, when the economic landscape is controlled by gigantic trans-national corporations, and energy is controlled by cartels. Which is the special case?
What about booms and busts? What about wars and the aftermath of wars? What span of American history would represent the general case?
To answer your question, population and the economy generally (if I may now use that word) grow together. The fact that GDP/capita has had an approximately constant growth rate over spans of decades is real world evidence that population growth does not lead to rising unemployment. So, one can reasonably surmise that immigration need not directly cause unemployment. If there were a labor shortage, then pretty clearly immigration could help the economy expand.
So, on balance, and despite my protestations, I was talking about something other than what looks like the usual general case over the last hundred years. Whether this constitutes a special case, or one of many possible more-or-less usual cases remains unanswered for lack of a sufficiently broad and detailed historical data base.
My main point was – and remains – that generalities are dangerous, the real world is messy, and dogmatic statements the reflect an absolutist view of economics that is highly questionable if you simply look out your window on any particular Thursday morning, ought not to be held up as examples of clear thinking and an appropriate way of viewing the world.
‘Cuz it seems a bit ad hoc.
And what makes this case different is the liquidity trap at the 0-interest bound, and the aggregate demand shortfall due in part to private deleveraging that causes the unwillingness of corporations to invest in either equipment or employees, compounded by the unwillingness of banks to lend at any level of risk when then can get an absolutely risk-free 0.25% on excess reserves from the Fed. Whether the collapse of the M1 multiplier is cause or effect remains a mystery to me.
We are hovering at the edge of a deflationary spiral, similar to the situation in 1929; but austerity rules the day, almost world wide. I am deeply pessimistic about this turning around any time soon – or even over the next several years. The incoming Repug majority in the House will only make it worse.