Unfortunately, most Americans have but a dim idea of the US, her political system or her history and her self-image derived from both.
I lived in a small town on the Mosel River for 3 years during my tour in Germany. During the 1980 elections, my neighbors pleaded with me to vote for Carter, as they were certain that Reagan would start WWIII.
My German at that time was quite good, as I was ending my 4th year in country. At my neighborhood gasthaus, I gave my neighbors a better understanding of American history and politics. In short, I brought them down off the ledge, but it took a couple of months.
The deal was sealed on Reagan's inauguration day, when the hostages were released. Shortly after, I was invited to sit at the stammtisch, a privilege not accorded to many foreigners.
It didn't hurt that I was one of their best customers. ;)
The Germans were utterly opposed to Bush, were convinced that he was a war monger and a (gasp) cowboy to boot. The fact that the Europeans gave Obama the peace prize right out of the gate tells us everything we need to know.
You are right, the average German is better informed about America certainly than Americans are about Germany and may even be better informed about America that most Americans, or at least those low information voters who returned Obama to office.