I wonder if, given the likely UKIP gains at the Euro elections, and maybe gains for other far-right parties in other countries, that the emergence of a strongly libertarian/more transparently corporate-owned EU would be a 'long game' for big capital, and would eventually lead to an anti-EU consensus amongst the left? The tories/UKIP only hate the EU because it is more lefty that they'd like the UK to be. If it pushed the other way, against minimum wages, workers' rights, state ownership, corporate taxation and so on, they'd be enthusiastic supporters. I don't think euroscepticism is an idealistic position about nationality & accountability, more down to the flavour of euro-government we currently have.
(and yes, I know it is already strongly neo-liberal and pushing things like break-up of the post office - but that's not the perception - it's all those 'uman rights, windmills and bananas that the public latch on to).