Probably not, but ideas like gay marriage seem to get their start in the US so a lot of the Bush-era US vs. EU rhetoric looks flimsy and silly.
I see it as more complicated than that. Someone on this thread mentioned Antonio Gramsci. While I don’t believe in the Italian communist’s ghost, I see his influence on modern leftism (which was really spawned after Russia fell to communism and Marxists in Europe were trying to figure out ways of bringing the proletariat to power in countries more stable than Russia was at the end of WWI).
When the USSR began to decline rapidly, its agents really came to the fore in Europe’s democracies in the form of its ‘Social Democrat’ parties, the most notable and successful in Sweden.
In America, their success was slower. First, our political system was more resistant to takeover and installment of Marxist principles. We have a constitution that actually has an almost theological reverence. The two main parties had strong anti-communist elements. While the Republican Party adamantly opposed big government solutions even on foreign policy in the early years, the Democrat party was less interested in social engineering beyond their obsession with eugenics and more interested in peddling influence and moving money around to special interests (particularly industrial unions).
Because of this, while a lot of successful Marxist ideas originated in the US (I’d argue most of the modern homosexual rights agenda was the brainchild of American leftists), it didn’t take root here before it did in Europe. The Netherlands had homosexual marriage first. Denmark had same-sex unions first.