Firstly, NO, the US is a country, the EU is not.
Secondly, even if the US as a country is tighter integrated and more financially successful than the EU as a union, the US is not a successful model example of a well functioning society that people in the EU would aspire to emulate, on the contrary, they'd rather preserve the status quo than turning into something resembling what the US has become.
Ok, well I guess if Europe is fine with a continued slide in global economic relevance, they can keep their status quo.
But something tells me that's not what Europeans generally want...