You ask what Americans think of Europe? I think you have to take into consideration who we are before you can appreciate our answers or lack of answers.
Many Americans are products (children/grandchildren etc.) of families that fled Europe for one reason or another whether it was political, financial, legal, religious, or otherwise. I'm sure if we could ask our ancestors what they thought of the particular country they had to leave, we'd be surprised at what they might have to say about "the old country". I'm sure it wouldn't be at all what we might expect.
Many of them came here and tried their best to put aside the ties that bound them to the old country. They changed their names, they refused to have their children speak the language of their old country. They dressed like Americans and did everything they could to become Americans.
Despite all this they were often not accepted even by the group of immigrants that immediately preceded them here. In spite of these things they still volunteered to fight for this country's interests even in the same countries that forced them to leave not so many years before. If they were too old to fight, many of their sons took up the cause without hesitation. We as their descendants have inherited some of their feelings. We couldn't help it. We feel some connection to the countries they came from. They rarely spoke, at least to us, of the reasons they had to leave. I think this is a big reason why many in this country feel surprised and resentful when we hear of lack of support from Europe. This can easily turn to antagonism as with the countries that opposed our actions most recently in Iraq. I believe we are somewhat naive in believing that Europe feels or should feel similar connections to us as we often do toward them.
I don't think there any choices in the poll that truly reflect the wide range of feelings that Americans have toward Europe. Sorry if this doesn't explain much but it's my opinion. Maybe if you had a poll about how Americans feel toward a certain country about a particular event?
I hate newspapermen. They come into camp and pick up their camp rumors and print them as facts. I regard them as spies, which in truth, they are.
Gen. W.T. Sherman