That would work if the economy was functioning normally, but say there is a fall in demand and workers are unemployed and factors stop production. Then there is a clear fall in demand and companies have to take cost cutting measures, at this point there are generally two options for employers cut wages, or cut jobs. At this point since the fact that the price of low end labour is inelastic doesn't matter as demand has fallen. This is where the minimum wage is a problem, it acts as a legal limit to wage cuts.

Or, stimulate consumer spending (or government spending [perhaps, through some manner of World War {that gravely disrupts international competitors}]).