No, that is a misunderstanding. What gp was talking about was a government surplus, which means government spending (investment + consumption + social) is small

No, that is a misunderstanding. What gp was talking about was a government surplus, which means government spending (investment + consumption + social) is smaller than government revenue (taxation). So in fact, with the kind of government surpluses that some (horribly misled) people are demanding, money will be sucked out of the private sector which will ultimately lead to less economic activity than otherwise. There is no sense in which the government can save money like you and I, because the government is the currency issuer. It has an infinite stockpile of potential money anyway, adding to that stockpile is entirely useless.