I've not been following the connection between currency valuation and threat of default. I'm not sure if it's just my not seeing some connection (certainly possible) or others conflating things that aren't actually connected. Why should I expect less demand for my dollar a week after a US default?
US dollars are the world's currency hub. Let's pretend that there was only one airline hub in the country, and we're going to say that it's Atlanta, because I always seem to use that as my connection. (Atlanta is a hub, but it's not the hub.)
Let's also assume that you have to use the hub, no matter where you fly. It's easy to see in this scenario that Atlanta will now enjoy a special status as an airport; everyone has to use it, even if they're not sending passengers to Atlanta. Now, let's say that the Atlanta infrastructure starts doing poorly - the ground crews don't get luggage from plane to plane fast enough, the controllers aren't good at scheduling flights - anything we can think of that will cause delayed flights. If flights are delayed often enough, then Atlanta's value as a hub goes down. If Atlanta's value as a hub goes down enough, airlines may try to move to a hub somewhere else. Atlanta, then, no longer enjoys all of the perks that come with having every flight in the country routed through them.
This is a cartoon, of course. Nor is the analogy perfect. But I think it gets the big idea across: when people do international transactions, US dollars are often involved. Even when neither side of the transaction is actually in dollars. US dollars are the world's reserve currency: the US is a large, stable economy, and the main instrument for storing dollars, US Treasury bonds, is the most stable security around.
If US Treasury bonds cease to be the most stable security around, then we have violated a basic assumption of the global economy. The rest of the world may try to move away from the US dollar as the world's reserve currency, which means the US would no longer enjoy the special status of being the world's currency hub.
Adam Davidson (who does Planet Money, which I linked to above) has a NY Times column explaining that in the short term, investors may buy more Treasury bonds immediately after a default, but in the long term, we would still likely lose our reserve status. See, "Our Debt to Society": http://www.nytimes.com/2013/09/15/magazine/our-debt-to-socie...
Just to add an additional factor, related to stability but not identical: the size and liquidity of the bond market also matters. An advantage to U.S. Treasuries is that the total volume outstanding is extremely large, and they are frequently traded. Therefore even very large trades can be executed quite easily, without completely swamping the market. If you want to buy or sell $50 billion of U.S. Treasuries, that is quite possible.
Other countries that are considered safe government debt for retail investors typically have much smaller and less liquid bond markets, which would make them unsuitable as a place to park China-sized amounts of money. An attempt to buy or sell $50b of Canadian bonds, for example, would involve 10% of the entire outstanding issue (and about 200% of average daily trading volume).
That's one issue with the Euro becoming a reserve currency as well. The total size of the Eurozone is large enough, and the total value of Euro-denominated bonds is large enough, but the bond market is completely fragmented, since a unified Eurobond hasn't emerged. Instead, if you want to park a large amount of money in Eurozone government bonds, you have to trade in all these smaller markets: French bonds, Polish bonds, Finnish bonds, German bonds, Italian bonds, etc., each with a different risk and liquidity profile.
