Small government is merely a buzzword that has been so overused it has become cliche. It is supposed to appeal to the angry working poor who imagine all government workers as loafers or incompetent, or far right ideologues who think taxes are theft, and community support is for suckers. It is an attempt to buy votes from segments of the electorate that are ill informed, or feel dysinfranchised and left behind, or want as little community contact as possible. It has been used so many times now it is often parroted unthinkingly by many, accepted with no introspection or investigation.
In fact the far right is enthusiastic about government, at least those functions that benefit them, and they are disdainful of those functions that are of no use to them. That is why items like national defense (and its resulting contracts), policing, and subsidies to business are strongly supported, and medical care, education, pensions, and employment programs are not.
Spin doctors have also wedded the notion of small government with the American mythology of the frontier, the steely eyed pioneer who needed nothing, as he was self-sufficient in all ways. It's an ad man's dream, a dodgy political proposition that will be disastrous for most, but wrapped up in images of Daniel Boone and Davy Crockett, and playing on the fears and ill founded suspicions of a browbeaten and largely uneducated working class.
And spin, as the last election shows, works.