Well yes and no. The way you establish a currency is as follows, traditionally: you assume political control over some area of land, and all political power is backed ultimately by military power (tho' cushioned by laws, courts, police, etc internally). Then you declare that everyone living on this land must pay taxes, and they must pay these taxes in... Seashells, or gold doubloons, or tons of flax, or whatever. Hey presto, you have a currency! Later on for convenience sake you can keep all your seashells in a vault and use paper tokens instead.

The thing is tho', you want other countries to accept seashells too, places where you have no political or military control. The way this happens is that those seashells can be exchanged for goods and services provided by your citizens, who need seashells anyway to pay their taxes, so might as well use them for everything else too. Therefore the value of a seashell on the currency market (i.e. outside your borders) is backed by the industrial power of your country.

So to sum up, a military backs a currency only in the sense that the military holds borders in which industry can operate safely - and not in the sense of military as ultimate debt collectors. At least, the Greeks better hope not.

Yeah, no country's going to compel the US to pay back its debt, given that the US probably spends about as much on the military as the rest of the world combined. Instead, they simply roll over the debt by buying more US Treasury IOUs. It looks far more like tribute to the military superpower, than the usual creditor-debtor relationship where the creditor dominates the debtor.

Of course, weak countries must pay their debts (even when a military dictatorship racks up odious debt), which is a lever to force them to ruin their societies through austerity programs.

It would take extreme desperation for someone like Japan to call in their held paper. That's an entirely plausible scenario though, given their debt loads.

However, the US could push a button and 'print' $2 trillion tomorrow morning in a monster QE3, and then hand Japan and China each a trillion dollars and nearly pay them off completely. All it would do is probably push the dollar index back down into the mid 70's, where it was 9 to 12 months ago. The bigger problem would actually be confidence, such a move would freak everybody out. Instead the Fed prefers to gradually inflate the value of Chinese and Japanese debt holdings away (which is also why China has taken such a liking to gold).