I think part of that reaction stems from the linkage between a household's budget constraint and the government's budget constraint. Really there isn't a linkage. Unlike households, the government doesn't have to repay ultimately its debt. The way I try to think about it or would explain it is that what you really want to think about is the debt burden. For the debt burden, the most commonly used measure is the debt relative to the economy.
What typically governments wouldn't necessarily want to do is to undertake fiscal policies such that this burden would be substantially increased for future generations. You can think of the idea of keeping a stable debt-to-GDP ratio as basically not passing on an increased debt burden. It's important to think about it in a ratio, because the incomes of future generations will be a lot higher than they are today. Their ability to service debt should be commensurate to what the burden is based on current taxpayers.
Maybe unfortunately, some economists have linked the balanced budget or debt elimination as the best indicator of sound financial management, when I think a much better one, and one that is most commonly used by budget offices and I would say most economists, is the debt-to-GDP ratio.