You're confusing consumers with businesses. Businesses can't operate that way and survive. Nice try though.
No, you're confusing the original argument.
The financial principles that apply to individuals and businesses are equally valid for the government: when income falls, spending should be cut back below the amount of cash coming in.
And like Ravi said, businesses draw down lines of credit when times aren't good.
But the original argument is a fallacy. Governments operate insurance pools - i.e. unemployment insurance, welfare - whereby individuals pay into pools when they are employed and drawdown on those pools when they are unemployed, which means government spend relatively more when times are bad. These are automatic stabilizers built into the economy, which dampens volatility in the economy. Governments cutting back during bad times is pro-cyclical, and makes the economy more volatile. Volatility in the economy increases uncertainty, which leads to higher long-term costs. Lower volatility decreases costs because it increases certainty. And over the past 40 years, volatility in the economy has decreased, in part due to an increase in insurance offered by the government.
If one says "governments should operate like business and households," OK, fine. Debt averages about 45% of the capital structure of a typical large American company. Businesses borrow to fund capital expansion. So governments should too, because governments "should act like businesses." Governments should borrow to fund expansion in the capital stock of the country in things like infrastructure and education. Households also borrow to fund capital expansions, i.e. mortgages to buy homes, to pay for university, etc. Households also borrow to fund consumption, i.e., when they are unemployed, for car loans, for credit card debt, etc. Governments should do that too. And they do. But the government should do it counter-cyclically. Governments should be running surpluses when the economy is expanding and deficits when the economy is contracting. And it should be paying for all spending over the cycle.