How does a national budget differ from a household budget? We are often told by pundits that "Country X cannot spend more than they take in in revenue, because a house that makes A and spends B will always collapse if B>A". Essentially the siren calls of a balanced budget as promulgated by the talking heads.

Sadly, despite even conservative economists like Friedman citing a k-percent rule and the necessity of inflation (since the number of people demanding money seems to continue rising), many entry level students get hung up on this concept. 

Essentially, what I'm asking is: 


  What are the key functional differences between a household budget (or other simple toy model) and a national budget and what's the best way to communicate this to people with only a passing familiarity with economics?


I'm looking for a way to effectively communicate to group of first year students that beyond just the ability to control the supply of money (monetary policy), and control income and spending more readily than an individual or household (fiscal policy), economic policy really has nothing in common with the ability to balance a checkbook, and the dramatic oversimplification is a disservice to the dismal science.
If you think about it, there is really not much difference between a government budget constraint and a household budget constraint. 

Both have uncertain income streams, which are labor and capital income for the household, and mostly tax revenue for the government. On the other side of the constraint, you will find consumption and saving for the household. The government will spend most of its income on (public) goods and transfers to households (social system).

Both can move income inter temporally using borrowing. However, neither can run a permanent deficit where it is "not expected to ever pay back", something that is typically referred to as a No-Ponzi-Game condition. As an implication, the "life-time budget constraint" will have to hold for both:

sum of all expected future income = sum of all expected future expenditures


I'm pretty informal here, you would typically rather derive "present value" of these constraints, but latex is not yet allowed here, and I'm already writing much.

What should government debt be used for?

We typically assume that households and governments have concave utility, they prefer consumption processes that are second-order dominating. Hence, they want to engage in smoothing of consumption over fluctuations.

Since all debt has to be paid back eventually, there is limited use of government borrowing. Most typically, one wants to stabilize consumption and output over business cycles, by financing consumption in busts and paying back in booms. Also, given an interest rate r, investments that promise a higher return than r can be financed through debt, as the government will not violate consumption smoothing.

Potential Difference

One potential difference is the commitment. Developed governments are typically more 
trustworthy, they are more likely to pay back there debt. Hence, they can borrow at cheaper interest than most households. As a conclusion, they can use debt more aggressively than households for the two purposes consumption smoothing and investment, as emphasized above.

tldr: Besides that, they're very much alike. Note also the Ricardian Equivalence, which is not at the heart of this question, but very much related.