To me it seems that the origins of the EU were financial. It grew out of capitalist interests which wanted to make trade easier between states. There was also a desire to make closer economic cooperation be the wedge which would eliminate future armed conflicts that were perceived to be mainly economic in origin (although xenophobia was the tool used to rally the masses).

Since these origins were highly technical and didn't affect most people directly, they got implemented without too much difficulty. Even the common currency didn't cause too much resistance (exceptions noted). But once these changes were flowing smoothly then the issue of labor migration became important. The same capitalist forces that promoted trade and commerce now sought to promote lowering labor barriers (especially strong unions in the western countries). But easier labor migration morphed into easier migration in general and thats where the economics ran into the cultural issues.

This is where the EU is now stuck: cultural resentment. I have no suggestions, but pretending the issue is something other than what it really is, will not lead to a solution.

I see only three possible outcomes, none really optimum.

1. One can have imperfect cultural assimilation as in the US, where those most able to fit in do so over several generations, and those least able remain abused.

2. One can reverse migration policies and try to turn back the clock. Apparently this is what Italy is trying to do at present. Leaving aside the inhumanity of the effort and its likelihood of failure, it also runs counter to the economic forces demanding cheap labor. This is the same issue facing the US right now. Cheap Mexican immigrants are "illegal" immigrants.

3. One can muddle along and hope that cultural differences will diminish over time. The young seem much less hung up over such issues as the older generations. The Irish and Italians were vilified when they first arrived in the US 100 years ago, but now being Irish-American or Italian-American is social acceptable and a source of light hearted cultural stereotyping (viz "The Sopranos"). The problem in Europe is that of language. In the US it was always understood that future generations would speak English and the native language would become secondary or forgotten altogether. Is Europe willing to make English the "official" language?

The social regulations (freedom of speech, assembly, religion, etc.) can be drawn from the US constitution and the large body of Enlightenment thought that preceded and has followed it. Brief and direct is best.

The political organization (which already exists, even if barely functional) depends upon solving the cultural issue. Is it one person one vote, or one country one vote? Are migrants members of their new country or their old one? How do you prevent the tyranny of the majority where more populace states have more influence? Unanimity was supposed to solve this issue, but has only led to paralysis. It must be squarely faced at some point - now would be a good time.

The goals. I don't think this has been properly treated in the EU. The US had the declaration of independence with it's "all men are created equal" as an implied framework, but the constitution also has:

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.

The goals are clear: justice, peace, welfare and liberty, now and in the future. I don't think that any countries which still have parties with "Christian" in their name are yet ready to adopt such universal ideals. So what do you want? A new version of the Austro-Hungarian Empire as a counter to a new version of the Ottoman Empire, or something else?

No consensus, no constitution.