I think a lot of the disgruntlement was likely to happen anyway. Europe is anti-american in part because it is viewed as a haven of mass-produced tat. McDonalds being the ultimate example - we hate it, but it still does well.
Tangent time! During the cold war everyone kept close to America - outside aggressors prompting unity and solidarity. But now there is no outside threat (other than terrorism, which doesn't really cut the mustard for this purpose, since it's so hard to solve). So countries are losing reason to stay close to America, don't feel the need to maintain good relations because there is no Soviet Russia looming on the horizon.
Britain was widely despised in Europe for the longest time. We were the outsiders (still are), the distant northerners who kept pushing people over and throwing our weight around. Contemplate the following quote:
That ambitious and greedy nation [Britain] has once more proclaimed to the world that she recognizes no law but that of aggrandizement of her own trade, achieved by her global despotism on the high seas; our patience is spent, our forbearance is exhausted; we must now turn our gaze to the dignity of our throne ... we must declare war on the King of England and on the English Nation.
That's taken straight from my copy of 'The Trafalgar Companion'. It's the Spanish declaration of war on the UK, from the Napoleonic wars, and one of my favourite, though hugely lengthy, quotes of all time. It's just so grandious and, for a Brit, amusing. Admittedly we British had a habit of attacking and capturing every spanish merchant ship we saw on the off chance it was a treasure galleon*, but still. However, when the German Republic started arming up, and the Central Powers formed their alliance, Britain and France started working together like old pals. They are showing an exhibition of the dresses worn by the then-Queen when she went with the Royal Family to Paris to help concrete the alliance.
I'm sure that if aliens from Zog were to invade and take over Africa, America's foreign relations would improve overnight... but for the moment nobody sees a 'need' for an American superpower, and thus isn't much interested in keeping good relations. I guess.
* Royal Navy officers were a greedy lot.