What makes you think that's true, that the EU brought/maintained peace? Is it trade?

To give a counterargument, if it is at all an argument, the trade relations with Hitler's Germany were very good. So much so, that they closed there eyes for what was happening and were very late to interfere. Hitler's rise to power was because he promised and kept his promise to not honour the treaty that forced Germany to pay enormous amounts of money to the "victors" of the First World War, bankrupting the country, much like is happening with Greece now (luckily there are a few and primarily leftist parties opposing the EU, but maybe only a similar extreme right-wing will follow through, if they find a "strong leader").

I think the differences and relative independence of the countries in Europe is one of it's strengths. Like a big laboratory of experiments with democracy and laws. Treaties between countries have always existed, there is no need for a new kind of federalist government, civil service, army or parliament. There are great things in Europe that just aren't possible if all countries do the exact same thing. It's like stalling evolution (and regression since services offered to only a few will be accessible to all and thereby overtaxed: it's just sabotaging the welfare state, very deliberately). It's neoliberal to the core: freedom to do exactly as told.

But maybe it shouldn't be discussed too much here, indeed. It was just that Obama got publicly involved, so maybe some from the US have an opinion on the matter.