There are a variety of problems with the analogy; neither the right nor the left really believe it applies if you even scratch the surface.
The left from a Keynesian perspective, of course, believes that increased spending during severe downturns will result in better fiscal health long-term. A very crude analogy would be investment as a long-term approach, although the way the investment works and when to do it is very different.
Less acknowledged, is that the right also doesn't believe in the analogy. There's no way to make the Laffer curve fit a family finance perspective ("don't worry, honey, I took a pay cut, but this will result in more money coming in").
In both cases, the relationship of the family to everything external to it, is very different than the relationship of government to everything external to it. So at best, it's a very flawed analogy.
But here's another reason not to use it. It REALLY opens you up to hypocrisy charges.
Freshman U.S. Rep. Joe Walsh, a tax-bashing Tea Party champion who sharply lectures President Barack Obama and other Democrats on fiscal responsibility, owes more than $100,000 in child support to his ex-wife and three children, according to documents his ex-wife filed in their divorce case in December.
“I won’t place one more dollar of debt upon the backs of my kids and grandkids unless we structurally reform the way this town spends money!” Walsh says directly into the camera in his viral video lecturing Obama on the need to get the nation’s finances in order.