The Eurozone is both unstable politically and economically: riots in France, Italy on the verge of bankruptcy, mutterings of a coup d'etat in Spain, failed euro constitution, Russians threatening Eastern Europe's energy supplies to win political advantage, millions of alienated Muslims, and the occasional left-wing or fascist nut job flipping matches into the powder keg via political assasination or home-grown terrorism.
Makes the US look like la repubblica serenissima.
The dollar itself is still a very stable currency compared to most other currencies, but people around the world with products to sell the U.S. simply want a lot more of them today than they would have accepted ten years ago for the same products and services. That's really all there is to it.