Yes it is a very fine line.
Yet taxation is not ring fenced.
And this 'we pay for you' is right, but to mark it so emotively and exclusively as financed from private sector work is not entirely accurate.
My uncle pays tax, as little as possible mind you, and it isn't borne from any UK operations.
He pays for me, and he isn't in the UK private sector. As an example.
The public sector is vital as an enabler, to damage it damages the UK as a whole.
It is interesting that, as a constitutional pillar, the UK has come to hate and disparage the services instead of being proud or respectful of them. This mallicious political streak seriously undermines the very concept it supports over time, the United Kingdom and it's establishment.
If your employer is not in a financial position to meet your expectations, then ultimately you cannot do anything except for increasing productivity.
With the public sector, people dissagree with the 'companies' ie governments spending priorities.
Imagine your boss wasting money on a security guard for your office when there is no requirement, for example.
This is not to say I am not sympathetic, because I am, but such simplistic lambasting isn't directly comparable. Neither is small and medium size enterprizes directly comparible to large business groups.
This is a seperate issue all together.