Could political leaders all agree to be bound by a pan-European vote (and unanimously implement the national instruments required to make what was voted upon legally binding?) Because that's what's required.
It takes a lot of political courage - but it's not courage that's needed, it's a sense of mission by the currently in power politicians to agree to give up some of their powers. In the long run, we're all dead. John Maynard Keynes
How much of a hot-button does the word and notion of "sovereignty" remain in Europe and different European countries? Is it routinely used by anti-Europeanists to rally nationalists against any movement to give up more of these powers? Or have Europeans in general -- if "in general" can even be applied in this context -- come to accept the manifest destiny of European unification (and the inevitable surrender of national sovereignties that that entails), squabbling only over the timeline and approach in which this unification is to take place? Truth unfolds in time through a communal process.
This is only different in England (not necessarily Scotland or Wales), where a lot of the people feel that they have more in common with some of the former colonies.
My guess is that a lot of people are dissatisfied with the EU as it is functioning now. They have a slightly contorted vision of what the EU is, and why it is not working as well as it could. And they're unable or unwilling to see that it is and will remain the main instrument for unification.
The potential to make the give aways on the national level and the unpleasant decisions an 'order from Brussels' for which the national politicians don't have to take public responsibility is the key point for the current situation. Der Amerikaner ist die Orchidee unter den MenschenVolker Pispers