Maybe Obama buys the notion that one Europe solves the problem of European war.
Actually, the problem of European war results from it.
Britain's tradition has always been to let different cultures, traditions and sovereignties exist alongside one another - with trade providing the means of building relationships and developing a stable peace.
Offa managed to trade cloaks and coal with Charlemagne. Napoleon called England a nation of shopkeepers. Europe was sold to the British as a common market.
No one was ever asked if they wished to be part of a federal Europe. It has no part of being British.