The following remarks are based on my comment at Tom's blog.
It's not self-evidently false that machines or techniques that reduce the amount of labor necessary to do a job will reduce the amount of available work. Arguments that it is are typical of vulgar libertarianism: they are equivocal as to how far the present system can be taken as a proxy for a "free market." To say that something "can't happen" under the present state capitalist system, because that's "the way the market works," is nonsense.
In a real free market system, the bargaining power of labor would be such that jobs competed for workers, instead of the other way around. And cooperative ownership and self-employment would be much more widespread than at present. Under those circumstances, decisions to change production methods would be decisions by labor itself to increase its own productivity, with labor internalizing all the good and bad consequences of the decision. Under those circumstances, it would indeed be a fallacy that workers would suffer from increases in productivity.
But in the present government-cartelized system, with legally enforced privileges for land and capital that force labor to sell itself under terms of unequal exchange, it's hardly likely that labor will internalize all the benefits of changing the work process. The presence of the state in state capitalism causes changes that might otherwise be mutually beneficial, instead, to be a zero-sum game.
So it's quite likely, under such circumstances of privilege, that the benefits of increased labor productivity would accrue to the owners of capital, while the harm would accrue to workers.
We don't live in a free market economy, or anything remotely approaching it. In a government-cartelized, corporate-dominated economy like the present one, the rules of "how the free market works" go right out the window. For example, it makes no sense to use Say's Law to "prove" that overproduction is impossible. As Joseph Stromberg pointed out, under state capitalism J.A. Hobson could be closer to the truth than J.B. Say.