Around here, it seems that the government workers make a lot more than the private sector.
Yes, obviously most government workers make more than most 'private' workers, but jmfcst is refering the tiny privileged minority who do (he's quite right) the lion's share of the spending. These are mostly private privileged, not government privileged.
Think of it this way:
Rich - 'private'
Very-high earning corporate elite - 'private'
run of the mill upper middle class - ordinary professions and the bulk of the educated government bureaucracy
middle class - ordinary government functionaries, a few middle managers in 'private' industry
working class - mostly private workers, and in fact most private workers are paid very little nowadays.
As you can see if you start to analyze these things, the first thing that you notice is that the State/'private' dichotomy is rather absurd. But certainly government workers make up a much higher percentage of the Middle and Upper Middle classes than they do of other the privileged elite or the downtrodden working class.