It is obvious that thousands would turn out for anti cut protests due to the sheer size of the public sector and indirect public sector jobs.
Thousands turn out for anti-cuts protests because thousands are adversely affected by it. By no means was it simply a case of public sector workers turning out. Equally not many people turned up for this protest because they're already getting what they want.
Generally speaking "the right" doesn't need to protest because they already have means to influence the system, while "the left" generally doesn't - which is of course why the system always changes to the poor and disenfranchised's detriment.