I once heard about the British Colonial Office. The time when it had the most employees was precisely the time when it was dissolved because Britain did not have colonies anymore. They were all just shuffling papers around all day.
I sadly don't have a source for that. Does anyone have a link, by any chance?
C. Northcote Parkinson, 1955. http://www.economist.com/node/14116121
"A glance at the figures shows that the staff totals represent automatic stages in an inevitable increase. And this increase, while related to that observed in other departments, has nothing to do with the size - or even the existence - of the Empire."
What I don't know is where Parkinson got his own figures from. Some of them are cited in the article, but I think not this one.
Anyway, the world you are so worried about is already here. A small number of people do continue to do important work that can't be automated. Most other work is unecessary busy work. Artists and musicians already live off of government largesse, either by taking "McJobs" that are artificially highly paid because of government minimum wage, or by actually being on welfare.
Since people can't wrap their heads around the concept of Basic Income, we end up with hordes of people paid to do stupid shit that doesn't matter. The endgame is that we're all government employees in a Dilbertesque hell. Moving papers from one pile to another and back again. Digging holes and then filling them again, since letting people decide what to do during the workday would be too disruptive.