EU has 'too many part-time Europeans' - Juncker
EU leaders say the 28-nation bloc lacks a coherent European vision and is being undermined by national self-interest.
"We have too many part-time Europeans," said European Commission President Jean-Claude Juncker. It is the Commission's job to draft EU laws.
He and other EU leaders spoke in Rome in a debate on the state of the EU.
Mr Juncker - a former Prime Minister of Luxembourg - said the old "shared sentiment" of common policy-making in the EU "has totally gone".
The man who chairs EU summits, European Council President Donald Tusk, said the EU's priority must be to make its external borders secure in the current migrant crisis.
He suggested that there was no point pursuing an ideal of a "European nation". He spoke of the need for "political common sense".
"The idea of one EU state, one vision... was an illusion," said Mr Tusk, a former Polish Prime Minister.
Eurosceptic parties, hostile to deeper EU integration, did better than ever in the last European Parliament elections, in 2014. They now account for about a quarter of the 751 MEPs.
A central theme for Eurosceptics is the fear that the EU is evolving into a European "superstate" sucking sovereign powers away from nation states. They point to eurozone integration as evidence of that.
Pro-EU politicians meanwhile argue that the 2008 financial crisis, the migrant crisis and environmental threats all point powerfully to the need for joint European action.
The Rome debate came as the UK prepares for a key in-out referendum on EU membership on 23 June.
Mr Juncker complained that "we have full-time Europeans when it comes to take. And we have part-time Europeans when it comes to give."
"In former times, all those implied in the project were full-time Europeans. Now we have too many part-time Europeans. That's the problem."
The Commission is struggling to get agreement among EU governments on an effective scheme for distributing migrants across Europe, to ease the pressure on Greece and Italy.
Four of the newer EU member states - the Czech Republic, Hungary, Poland and Slovakia - object to any mandatory quota system for migrants. They say it would be hard for them to integrate non-Europeans, especially Muslims, many of whom anyway want to settle in Germany or other richer countries.
Without mentioning those countries, European Parliament President Martin Schulz complained about leaders "who are coming to Brussels and giving interviews 'I have to defend the interests of my country in Brussels'."
"Often these are member states who get a lot out of the cohesion funds of the European Union and are not attacked, but supported by Brussels," he said.