A few months ago at the height of the Greek debt crisis, I wrote that the lesson of history is that the EU is a survivor, i.e. European integration wasn't going to collapse no matter what the outcome. The Eurozone countries would find a way to keep Greece inside or else the country would leave the Eurozone willingly or unwillingly. Breaking the taboo on temporary or permanent exit might even increase Eurozone integrity because other governments would take note.
When the anti-austerity Prime Minister Alexis Tsipras gave in to the inevitable and accepted harsh terms for a new bailout, the way was open to EU political economy as usual: all-night meetings, ambiguous implementation plans, wiggle-room galore and the potential for political resurrection. Tsipras, having fought the good fight for his country, won a snap referendum of popular endorsement and just a few weeks ago won a snap parliamentary election having maintained Greek dignity. The problem of Greece's huge debt remains to be resolved long term but no one doubts that, along with that country, the Eurozone and European integration have been rescued. Greece's travails are not only off the front pages, they're hardly worthy "news" anymore.
The same pattern generally speaking will play out in the sudden, massive influx of refugees/asylum seekers and economic migrants of the past several weeks. European integration as a historical process is beyond a point of no return. Degrees of integration in its various aspects will wax and wane (e.g. national sovereignty vs. European decision-making) and certain structures or functions of EU life may go into rigor mortis (one or more countries exit from the Eurozone or collapse of Schengen internal border-free travel). One or another country might even opt out of the EU, e.g. a British "Brexit" at stake in a referendum to be held sometime before 2017.
But even then, not all ties with the EU need be broken. For example, Common Market and other access for a departing country could be set up in some new framework, of which there are already several: association agreements and neighborhood agreements link a variety of countries such as Turkey, Israel, Jordan and even Algeria and Libya to the EU. Brexit would not mean a total overnight divorce and the British would find that divorce is more painful for them than for the Continent, perhaps choosing to think (and vote) again. Brexit would be the start of a long negotiating process ending in another British special relationship.
When the Greek crisis broke, media commentators rushed to outshout each other that it was the deepest crisis in EU history; the Eurozone couldn't survive and without the euro all was lost. Surprisingly, the refugee crisis brought even veteran observers to similar views. One Brussels specialist said, "Schengen is the essence of the European Union...if Schengen were to collapse it could mean the whole idea of the EU is no longer valid." At a Council on Foreign Relations meeting a very eminent economist and international bank and institution advisor said, 'this could be the most dangerous crisis since the beginning of European integration in 1951 when the European Coal and Steel Community was created.' German Chancellor Angela Merkel as usual spoke the language of responsibility: the refugee issue is a deeper problem for the EU and will take longer to resolve than the Greek debt crisis. Among other things this in a word put the Greek crisis into perspective.
EU internal relationships are under severe stress in organizing what to do with and how to absorb the refugees and would-be migrants. The first issue is attending adequately to their daily lives. In the process, issues of human rights, national sovereignty vs. European solidarity and practical organization must be resolved. The outcome -- the lives refugees will live after the crisis has receded -- is uncertain. What is certain is that the refugees will not be allowed to starve and will be settled (some economic migrants may be sent back) in a reasonably humanitarian way although not without conflict with local populations in some places. As a result of EU member state conflicts over what to do, European integration as a whole may end up more or less, worse or better-off. But the EU is unlikely to collapse. It will adapt and continue muddling through stable times and reacting to sudden crises toward some ill-defined end point.
The EU is just too important for European civilization; its integration has become too elaborate structurally and functionally; and too successful in various respects, that Europeans should let it go. Europe will survive the current rise of ugly political populism in certain EU member countries. It will absorb a large number of new arrivals and go on.