What do you specifically even mean for the United States as a society to "save" money? Getting dollar bills and stuffing them into a vault? Are you saying that in an ideal world without feckless politicians, the government should tax more than it disburses, build up a pile of money, and then pay out extra money?
The further you draw the analogy out, the more ridiculous the idea of equating government finances with household finances become. It's just folk economics. And that's ideology-neutral: you can be a Keynesian, monetarist, goldbug, whatever and still should reject that position.
Generally speaking, when a country saves it takes money and invests it in things that will make more money, like factories or research. The reason that China is growing so fast right now is that it has a very high savings rate. On the other hand, there are less obvious good places to invest money in a developed economy.
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.
The further you draw the analogy out, the more ridiculous the idea of equating government finances with household finances become. It's just folk economics. And that's ideology-neutral: you can be a Keynesian, monetarist, goldbug, whatever and still should reject that position.