The south didn't vote for Lincoln and attempted to secede with the US president initiating the war to overturn the local state's right to do so.
I think a lot of europe's problems would be fixed by making the office of the EU presidency a directly elected office in a similar fashion to the US presidency. The EU would still require further centralization to maintain the eurozone and to further deepen the EU single market. They are just required to maintain our current levels of wealth and to fix the banking crisis that has never really been solved in the EU.
A single individual with a policy platform that has gained legitimacy through campaigning in all EU member states would settle questions related to the future of the union and will be best placed to implement and direct policies that benefit the majority of the EU population.