This ties into everyone's favorite term "Luddites", but I would be willing to bet most folks don't know the history of this term.
"In economics, the lump of labour fallacy (or lump of jobs fallacy) is the contention that the amount of work available to labourers is fixed. It is considered a fallacy by most economists, who hold that the amount of work is not static. Another way to describe the fallacy is that it treats the demand for labour as an exogenous variable, when it is not. It may also be called the fallacy of labour scarcity, or the zero-sum fallacy, from its ties to the zero-sum game."
Also from Wikipedia:
"The Luddites were 19th-century English textile artisans who violently protested against the machinery introduced during the Industrial Revolution that made it possible to replace them with less-skilled, low-wage labourers, leaving them without work. Historian Eric Hobsbawm has called their machine wrecking "collective bargaining by riot", which had been a tactic used in Britain since the Restoration, as the scattering of manufactories throughout the country made large-scale strikes impractical.The movement was named after Ned Ludd, a youth who had allegedly smashed two stocking frames 30 years earlier, and whose name had become emblematic of machine destroyers. The name evolved into the imaginary General Ludd or King Ludd, a figure who, like Robin Hood, was reputed to live in Sherwood Forest."