That's odd, because in Canada, we tend to vote for our choice of government, so, you see, we are society AND we are the government, too. When did Americans start thinking of government as something monolithic and out of their control? Because in a democracy, you get to get rid of your government if you don't like it. Just random thoughts, of course.
I'm certainly not one to contradict such a brilliant thinker and revolutionary as Thomas Paine, who repeatedly risked his life by publishing "seditiously libellous" pamphlets and books such as The Rights of Man, advocating, among other things, representative government and social measures to relieve poverty, including a progressive tax. So perhaps you have misread his distinction between society and government. He certainly did not shy from advocating government action to improve society and the common good.
Laying snarkiness aside, our parliamentary system does make it easier to get rid of our government, all it takes is a vote of no confidence, and it's instant election. I think it is more difficult with the US system. Maybe that accounts for the pushback against "government." But still.