But even as Hussein offers me a sharp, fresh juice, he’s downcast. When I ask about the subject on everyone’s mind here — the migrant flood into Europe — he laughs. “We were just talking about this!” he says. Several of his friends just passed by to say farewell.

They heard that German Chancellor Angela Merkel was welcoming Iraqis. “Each one said, ‘I’m traveling,’ ‘I’m traveling,’ ‘I’m traveling,’ ” says Hussein. All want to be smuggled to Europe.

Conversations in the Iraqi capital, between the rich and the poor, travel agents, taxi drivers and demonstrators in Friday protests, show a city galvanized by the news from Europe. The violence and decrepitude here are nothing new, but now there is a perception of an opportunity for an alternative, and many are seizing it.

Fleeing Iraqis already form a significant chunk of the migrants streaming into Europe. The International Organization for Migration says roughly five times as many Iraqis — about 5,000 people — have arrived illegally in Greece through July this year than in all of 2014.