One particular analogy people bring up when talking about the government's budget is a "family" analogy. They will claim that we are like a family with $40,000 in income each year, but who is spending $70,000 and has $250,000 in debt, or some such figures. There are multiple reasons, however, that this analogy is flawed and leads to false conclusions.
First, macroeconomics. A family is tiny relative to the economy. Regardless of how diligently they save or how wildly they ring up the credit cards, the overall economy does not change meaningfully. This means that the chances that they will be laid off, hired, or see a big boom in orders at their shop are unaffected by their own spending habits. The government, however, is not small relative to the economy, making up more than a third of it. If the government slashes spending...well, there is a lot less spending. People get laid off. Tax revenues go down. People wind up on the dole. After all is said and done, it is not even clear that the money saved via the reduced spending isn't lost completely due to the reduced revenues and new safety net spending. Even if the government comes out ahead, it is only marginally so, and at the great cost of millions being laid off.
But won't the private sector pick up the slack? Not when we are in a liquidity trap. If you don't know what that is, you simply do not understand what has happened in our economy the last four years. The mechanism by which the private sector normally "picks up the slack" is by falling interest rates, which stimulate investment. But when you are in a liquidity trap and risk-free interest rates are already essentially zero, they can't fall any further (since you can hold cash instead, they can't really go negative). So if the government cuts spending in a liquidity trap, it just adds more slack to the economy, and employment and GDP fall.
A second problem with the family analogy as normally presented is that those who present it seem to think the family income is fixed. They never pause to consider that one solution might be to work more. Indeed, a nearly perfect analogy exists between the family members' hours worked and tax rates, as both are essentially proportional to income and more or less voluntary. Given that we have the third lowest taxes in the OECD, perhaps our "family" problem is that mom and dad only work 25 hours a week each. Likewise, spending on automobiles for the family and defense for the government are pretty similar in size. Since our defense spending is second highest in the OECD (per GDP), perhaps the family's problem is that mommy drives a $40,000 SUV and daddy has a BMW.
Yet just about every time someone presents this analogy, they never consider the macro effects, ignore the SUV and beemer, and not only dismiss the idea that mom and dad are lazy and could solve the entire problem if they just worked full time, but actively argue that mom and dad are just so hard-put that if they worked more, their productivity would drop so much that they would earn even less overall! So instead of addressing these issues, the family must raid Junior's college fund, ignore the leaking roof, and skip their annual check-up. Clearly, that's a one-way ticket to prosperity.