There is now a well-established pattern to the European Union’s response to crises. First, there is denial of the problem. Then there is squabbling over who should take responsibility, and then a series of half-baked attempts at a solution. Finally, the member states agree on a plan of action that may not remove the underlying issues but at least holds the union together. This was how the EU handled the euro crisis, and the same playbook has been followed in the migration crisis—a crisis the bloc initially chose to treat as a local Italian and Greek difficulty. It now hopes to resolve it via a comprehensive deal with Turkey that EU leaders hope to seal at a summit this week.

This migration crisis is the biggest threat to the survival of the EU because, in contrast to the euro crisis, there is no European Central Bank to make the problem go away or, at least, hide it from voters. Instead, voters see a problem that already appears unmanageable and unending. What the EU is confronting isn’t just the tragic displacement of refugees from Syria but a multibillion-dollar people-smuggling industry with an apparently inexhaustible supply of potential customers from the fast-growing populations of Africa and Asia. These smugglers are taking advantage of the EU’s deep commitment to human rights to make a mockery of its efforts to control its borders.

The proposed deal with Turkey is a potential watershed because it marks the first serious attempt by the EU to destroy the people-smugglers’ business model.

Under the deal, everybody who illegally arrives in Greece will be sent back to Turkey; and for every bona fide Syrian asylum seeker sent back, the EU will allow one Syrian refugee to come to the EU—but crucially, not those who made the illegal crossing. They will go to the back of the asylum line. The goal: anyone who pays a smuggler won’t only lose their money but also worsen their prospects of resettlement.

Of course, the deal is controversial, not least because of the manner in which it emerged. When European leaders gathered in Brussels for a summit with Turkey last week, they were expecting to sign up to a less ambitious deal negotiated by European Council President Donald Tusk. This would have seen only those ineligible for asylum returned to Turkey. Syrians would have been allowed to stay. But at an 11th-hour meeting between Turkish Prime Minister Ahmet Davutoglu and German Chancellor Angela Merkel, Turkey offered to take back all migrants in return for an extra €3 billion ($3.34 billion) of aid and a deepening of Turkey’s relationship with the EU.

To some Europeans, this deal smacked of a desperate capitulation by Ms. Merkel ahead of Sunday’s regional elections in Germany in which her party was expected to fare badly. But Turkey also had good reasons to strike a deal. Its own negotiating leverage had been badly weakened by Austria’s decision—ironically, opposed by Ms. Merkel— to close its borders to new asylum seekers, thereby causing a domino effect of border closures along the Western Balkan migrant trail that has left thousands stranded in Greece.

The unfolding humanitarian emergency on the Greek border with Macedonia also threatens to undermine the smugglers’ business.

Even so, there are four major obstacles to a successful deal. One is legal: United Nations High Commissioner for Refugees has warned that mass expulsions are illegal under international law and could only be allowed if Turkey met the international standards on the treatment of refugees to qualify as a safe country.

Meanwhile the biggest hurdle, say EU officials, may lie in Turkey’s demand that the EU accelerates its application to join the bloc. That would require Cyprus to drop its veto on five of its so-called “accession chapters,” or areas of policy discussions that are part of the road map to becoming an EU member. The government in Nicosia is unlikely to do that while Turkey is, in the eyes of international law, illegally occupying the north of the island.

A second obstacle is Turkey’s demand that the EU waives visa restrictions for its 80 million citizens by June, four months earlier than previously envisaged. This would still depend on Ankara complying with 72 conditions already laid down by the EU, of which it has so far fulfilled only 10. But many European governments are wary that the European Commission may try to water down its assessment of these conditions to facilitate a deal.

A third challenge is what to do about the asylum seekers already stranded in Greece. In theory, their applications should be assessed in Greece and those qualifying for protection resettled across the EU according to quotas controversially agreed last year. But with four countries in Eastern Europe refusing to participate in the resettlement program, this may be impossible to enforce.

Does this mean the EU’s response will fall short again? Not necessarily. The stakes are so high that compromises may yet be found to ensure the right message is sent to the smugglers. The challenge then will be to ensure that what is agreed upon is actually delivered. But the lesson of past EU crises is that even a successful deal will likely only buy time—in this case, until the smugglers figure out a new way into Europe.