I'm in a small local authority. Our income from commercial operations (car parking mainly) is greater than our 'grant' from central government. Most other local authorities have also had their central government funding cut drastically as well - and now council tax makes up around 25% of their budget, add in local business rates and commercial income. And you are looking at a vast amount of money in local government not being centrally funded.The beauty of increasing NIC from the government's point of view (at least employer's NIC, which I would presume they are on about) is that it only affects the private sector. Effectively, employer's NIC doesn't affect public sector workers because the government is paying it to itself. So they can hit the private sector without affecting the public sector.
So, it is not correct to say that NI does not affect public sector workers. We pay our NI to central government, not to ourselves. So, and employers NI increase will lead to more cuts to local services - so of course the public sector will be hit.