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...