At least in most capitalist countries, the "middle class" is actually the decently-paid subset of the Working Class, in the Marxian sense, whereas the "working class" actually means the outright struggling subset of the Working Class.
Point being, not only do the middle class provide universities and health-care by paying taxes for them, they make up a large portion of the actual professional labor force at those institutions.
I'm very, very left-wing, but having newspapers print long articles more-or-less pointing and laughing at any of the workers who actually keep whole countries running is pretty goddamn insulting, and that includes when they label those workers "middle class" or "hipsters".
Dignity in labor applies to the white-collared, too.
Well, what if the middle class stopped working? Have we forgotten the teachers strikes? Admittedly it doesn't have the same immediate effect as the miner's strike turning the lights out. But healthcare and education are very stereotypical middle class occupations.
Trying to organise teachers to strike indefinitely is basically impossible as no teacher wants to damage the chances of their students. So a replay of the miners' strike of the mid 1980s will not happen (and I'm sort of glad about that given the permanent polarisation that action caused in the communities most affected). In the modern UK, an indefinite school teachers' strike would cause significant disruption as most families have both parents working.
My colleagues might manage a token one day strike now and again, but basically that is your lot. What is termed 'action short of a strike' can actually be more effective in certain circumstances. Cutting off the flow of data really bothers the management but the everyday work of the institution continues; students continue to be taught, to have work marked and to receive feedback designed to improve their understanding of the material.
Their taxes are theirs. It's through generosity that social programs are created and paid for through the general revenue.
Although admittedly it has now backfired, as it's now easier to have children on welfare than it is for many working would-be parents.
The working class WILL stop working and in the very near future, as basic jobs such as checkout staff, or taxis, become automated. It's an impending crisis.