That's a tantalizingly simple and intuitive comparison that everyone can understand and relate to. Unfortunately a nation's economy is so utterly unlike a household economy that the comparison is downright dangerous, because it leads to harmful false assumptions like "national debt is always a bad thing", "a nation must always 'earn' more than it spends at all times", and "an economy can never grow in a nation with debt".
I'm no economic wizard but it really surprised me that how everyone in Europe and many in the States are prescribing austerity, when basic history from this very century frequently demonstrates that austerity can lead to economic damage. Yes you can always find programs that can and should be cut back in any developed society, but considering debt to be the central and only problem in a situation where the debtor defines the very money it "owes" seems a little shortsighted to me.