Of course, a similar argument can be made about ANY labor saving technology introduced during the past 200+ years. But since we know that the demand for labor did not go down during those 200+ years, this should have raised doubts about the validity of this kind of arguments.
In reality, however, the introduction of a new technology simply moves labor from one sector to another: from agriculture to smokestack industry, from smokestack industry to assembly line industry, from assembly line industry to services, etc. Any labor stats can show that. There are good theoretical reasons as well - demand for labor is function of supply of labor, rather than the other way around - especially in a Keynesian economy.
What really surprises me is the persistence of these arguments despite ample evidence to the contrary. Evidently, such technology-displacing-labor arguments are advanced to further ideological and propagandistic positions: the new technology spells either doom (Luddites) or salvation (technophiles). By the same logic, irrational opposition to water fluoridation is being packaged as concerns for the environment (http://www.fluoridealert.org/).
Wojtek