To this, my excellent former co-blogger Winterspeak responds that since the United States has a monopoly on the currency it issues, it can't default--it can just keep running the printing presses. There are a couple of problems with this. In some sense, I think it confuses cause with effect: the government gets to borrow in a currency over which it has a monopoly, because it has been a fairly credible steward of that currency. If it inflated away its debts on the scale of, say, a Latin American nation, it would not be able to borrow in dollars any more. And since it needs real goods and services, not little green pieces of paper, that matters.
For his point to be right, you need to believe that the government can end up financing the entire debt by seignorage, which is the revenue that the government gets from issuing currency. In the case of the United States, that revenue is currently pretty considerable, because so many people overseas use dollars as their emergency bank account; essentially, they give us goods and services in exchange for dollars, and then stash those dollars under their mattresses. But that's because we don't inflate the currency.
In the case of a hyperinflation, essentially, the government gets a slight discount, based on the fact that it knows how much money is in existence, and you don't. It prints the dollars, and uses them to buy goods, and then the oversupply of dollars pushes up prices still further. But the discount is actually pretty small, and hyperinflationary seignorage turns out to be a very inefficient way of generating tax revenue, especially in a world where there are modern financial markets monitoring government behavior. The much maligned Laffer Curve is actually a pretty effective model at describing hyperinflation; it's very easy to get on the wrong side, where inflationary expectations and deadweight loss start killing the revenue you can raise. It is possible to end up in a place where, as with the Zimbabwean dollar, your monopoly right to print your currency becomes worthless, because the demand for that currency is essentially zero--no one will give you goods and services in exchange for your paper.
If you're talking about a past stock of debt, it makes some sense to talk about it solely in terms of dollars--really, accounting entries. But of course, the reason the government borrowed the money is that it needed to secure real goods in the economy, and its citizens didn't want to reduce their consumption enough to pay for it all with their taxes. Sometimes that's a one time event, like a war, in which case inflating away your debt looks quite attractive (immoral, possibly--but then, lots of attractive things are immoral, n'est ce pas?)
But more often it's an ongoing problem. In which case, it's hard to aggressively inflate, because within a very short period of time, your ability to borrow in your own currency at attractive rates will fall off. So if you're going to hyperinflate, you need to be prepared to quickly close the gaps between the real goods and services you want to consume, and the real goods and services you want your citizens to give up in order to pay their taxes. In other words, you need to be prepared to stop running a budget deficit--or to resort to increasingly desperate tactics like Argentina's nationalization of its private pension regime in order to loot the accounts.