Ignoring the Euro, that's an oversimplification. It's "faith and credit." And there is a statutory link between the credit of the US -- the value of US debt -- and the earning power of US citizens -- that's a bit more than faith.
Estimations of the strength that earning power, the ultimate value of the dollar, the likelihood of the US Gov't to truly default, etc do enter the realm of speculation, which is lumped together with "faith," but only carelessly.
The term ‘full faith and credit’ shows that they are linked, even if only in peoples’ minds. Once the ‘credit’ is gone, as in the US downgraded or outright default, the ‘faith’ erodes rather rapidly until there is none left. The dollar will become as worthless as Confederate money was after the Civil War. They have destroyed an entire nation’s wealth in less than a decade................