Actually, if companies start cutting employees hours and using other methods to skirt providing them adequate compensation or employment benefits, you'll probably see exactly that.
I can think of no better way to bolster the ranks of unions actually.
So the government makes hiring more expensive, forcing businesses to cut hiring and hours, and the solution is to form organizations dedicated to making hiring even more expensive? A workforce unionizing will not give companies larger budgets to hire people with; only higher revenues will do that. Faced with both hostile government action and hostile private action (assuming, as your hypothetical does, that the union is organized specifically to confront the employer over wages and benefits--which does seem to be the case more often than not, though one could conceive and wish for a more productive and less parasitical role for unions to play), why would an employer stay here and build his house on quicksand?
Also, unions' major weapon was not the solidarity of their own membership, or even their power in Washington in times of Democratic ascendancy. It was the solidarity of others outside their union--other citizens who would simply not cross a picket line to patronize a business with a striking workforce. Maybe some people still express that kind of support for the labor movement, but by and large, the public image of the labor movement has degraded significantly over the past few decades, and the image of many parts of corporate America is much improved. (The financial sector still gets a fair amount of well-deserved opprobrium, and some individual companies like Wal-Mart are polarizing, with many supporters and detractors, but Apple is the biggest company in the world right now, is nonunionized, and everyone seems to have a pretty good impression of it.)