Solidarity didn't win out in the Euro crisis and I am not optimistic it will win out in this instance.

That's not quite true. The framing in the Euro crisis was (and is) that Greece needed money and the taxpayers of the Eurozone gave that money in order to help. Most people are in favour of helping Greece in solidarity and don't quite understand why the Greeks are being ungrateful. We, the left, did not manage to successfully counter this narrative, so far that is. We are working against an economic dogma that has been dominant for a generation, though.

In the issue of granting refuge to people fleeing the wars of the Middle East and Africa there is no such dogma. It is a matter that people can understand without a course in economics as it hasn't been taught for 35 years. You watch the news of the atrocities and then you hear of people who give up their homes and all their possessions and try to escape. That's not that hard to understand and to have empathy with. No, people aren't selfish and evil. People often are scared, and then they become selfish and evil. It is a matter of political activism, if they need to be scared, though, and what or whom they fear. If we remain passive, your scenario might happen.