Europeans are much less likely to chase the Euro than their US counterparts are going to chase the buck.
Language is one part of the issue, another is that we have a completely different look at distance. I'm living in Romania right now, I don't even know a single other Dutch person that has moved to Romania.
In the US you'd be in the company of 1000's of people from 'out of state', but you're all Americans. In Europe the chances of getting a job differ greatly depending on where you're from and where you are applying for a job.
A Romanian in NL or France would have a harder time finding employment than a local (and would get paid substantially less when they do find a job), a guy from Michigan or even Canada in San Francisco would have roughly the same chance of finding employment as a local and would earn roughly the same amount of money (that's anecdote based, not 'data' based so correct me if you feel this is inaccurate).
Part of all this is culture, part of it is stigma, xenophobia, language, perceived quality over the last decade or so of hiring people from different countries and with different backgrounds.
The US is simply much more homogeneous than Europe will ever be, even though there are large differences between say California, Colorado, Florida, New York and Wisconsin the differences between the people from those places are not all that large mentality wise and so on. You participate in a single set of elections with parties that are present everywhere.
Compare that to Spain, France, NL, Sweden, Poland, Romania and Greece to select a few examples, and the people from those countries, each with a fairly unique cultural identity. No unified elections (some of the parties don't even have parallels across a border with a next door neighbour). There is no shared history, the history books are usually written from the perspective of the country where it will be used for teaching rather than from the perspective of Europe or something a bit more objective than the local country.
I don't think the 'Federated States of Europe' will ever feel as closely knit as the USA does.
Think of the differences between the groups of states on both sides of the American civil war, now multiply by 15 or so and then take all the possible interactions between those parties. That gives you an idea of what the shared history looks like for Europeans.