Read Paul Krugman. Governments don't rev up the economy by spending less. The family analogy doesn't apply.
The answer is that an economy is not like an indebted family. Our debt is mostly money we owe to each other; even more important, our income mostly comes from selling things to each other. Your spending is my income, and my spending is your income.
So what happens if everyone simultaneously slashes spending in an attempt to pay down debt? The answer is that everyone’s income falls — my income falls because you’re spending less, and your income falls because I’m spending less. And, as our incomes plunge, our debt problem gets worse, not better.