Note that almost all of the problem countries ran trade surpluses before joining the Euro, and that the different regions had a lot better balance of trade as a whole. What then happened was that the fixed exchange rates made the automatic rebalancing, that competing floating currencies have, stop working, and inbalances aggregated in the system. These inbalances took a form that is perceived as overspending, but that is a much too simplistic view.
The economic problems of US are a lot less severe than those in the Euro area, precisely because US has a different way of equalizing bad balance between regions - namely taxes and federal spending. There are also no danger of default, since US can fulfill the obligations it has by printing money. That is also not on the table in the Euro area.
Printing money to pay debt is a form of default that would result in loss of credit ratings. The US is still within the realm where they can be reasonably expected to pay their debt through conventional means (taxation and reduced spending), which is not the case for some countries in the eurozone.
The economic problems of US are a lot less severe than those in the Euro area, precisely because US has a different way of equalizing bad balance between regions - namely taxes and federal spending. There are also no danger of default, since US can fulfill the obligations it has by printing money. That is also not on the table in the Euro area.