Murray Rothbard has already refuted this notion in his treatise Man, Economy, and State by pointing out that if wages can't fall legally because of minimum wage regulations, this is due to government intervention. On the other hand, if it is due to voluntary labor contracts, then any unemployment that results is not involuntary because workers and labor unions could always renegotiate a lower wage.
It turns out that this is exactly what is happens during times of economic downturn. For example, performing arts unions worked together with Broadway production companies and agreed to be paid lower wages for a period following the 9/11 terrorist attacks in New York City which caused the tourist trade to fall off for awhile.
Now it is reported that a number of labor unions are doing the same thing in response to the Great Recession. These workers and their unions recognize that sometimes one has to agree to a lower wage to keep one's job when the demand for labor falls. This is precisely how markets clear and one important way malinvestment is resolved in a recession.