The NewsHour's William Brangham reports tonight from that border region, in Roszke, Hungary

　　WILLIAM BRANGHAM: For hundreds of people fleeing Syria and other parts of the Middle East, their journey had come to a halt in this mud-caked field. This isn't an official camp. Those are several miles away and filled to capacity. So this is where the Hungarians put everyone else.

　　Dozens of armed police lined the edge of the field. There weren't enough buses to take everyone to other processing centers elsewhere, and so frustrations boiled over. This woman pleaded with police to let her elderly wheelchair-bound mother onto a bus. Police said no repeatedly, so the family gave up, saying they'd walk back over the border to Serbia.

　　For others, the waiting was just too much. A large group pressed against the police line and then finally broke through. At least a hundred people took off across the field in a desperate rush. Police tried to tackle some, but the majority got away. Most disappeared into the cornfields. Some shouted they'd walk to Budapest, more than 110 miles away.

　　This young boy Hassan made it through the cornfield and said he wants to get to Germany. He said his family's home in Syria was destroyed in the war, they had been forced to flee, and being trapped in Hungary was just too much.

　　HASSAN: It's been two days, and the rubbish is piling up, and there's no toilets, nothing. They just throw food at us, and say to us, stay, stay. We don't want food. We just want to cross peacefully. We mean no harm. We just want to get to our destination.

　　WILLIAM BRANGHAM: For those who didn't escape, the seemingly endless waiting game continued.

　　Here at this border, this fence, which was put up by the Hungarian government, it stands in stark contrast to the response of other European nations. As Hungarian Prime Minister Orban calls for the rest of this fence to be built faster to keep refugees and migrants out, others in Europe are debating whether and how to let more people in.

　　Germany alone is expecting some 800,000 applications for asylum this year. That's equivalent to roughly 1 percent of its current population. Chancellor Angela Merkel has called for a mandatory quota system across the continent, where different nations would be assigned different numbers of people to take in. It's an idea she reiterated today when she met with the Swedish prime minister in Berlin.

　　CHANCELLOR ANGELA MERKEL, Germany: I think we need a fair distribution in Europe. Binding quotas or numbers are necessary on sharing out refugees who are entitled to asylum, and who then are distributed fairly among the member states. Unfortunately, we are far from that.

　　WILLIAM BRANGHAM: Hungary and other Eastern European nations have rejected any such proposal. But the president of the European Union, Jean-Claude Juncker, will unveil a plan tomorrow to find homes for more than 120,000 refugees. And in Washington, the Obama administration said it is — quote — "actively considering" ways to assist, including resettling refugees in the United States.

　　JOHN KIRBY, State Department spokesman: In this year, 2015, we have resettled something like 70,000 refugees from all around the world, not just from the Syrian conflict. We also have to balance that against the proper vetting procedures to make sure that, particularly when we're bringing in people from that part of the world, that we're doing it safely and securely. The American people would expect that.

　　WILLIAM BRANGHAM: Meanwhile, in Paris, ministers from 60 countries met today to address the root cause of the crisis, the ongoing wars flaring in the Middle East. The head of the Arab League agreed with this broader focus speaking in Cairo.

　　NABIL ELARABY, Secretary General, Arab League: I must pay tribute to all European countries, and particularly Germany. However, I would like to emphasize that this is not the resolution of the problem. What is needed is to end the conflict in Syria.

　　WILLIAM BRANGHAM: But as diplomats around the world debate the appropriate next steps, the human wave keeps pouring onto European shores, including hundreds more that landed today outside Athens, Greece. And back in Hungary, even as more people continue their wait for a ride out of here to anywhere else, the flow of people coming across the border from Serbia also continues.

　　For the PBS NewsHour, I'm William Brangham in Roszke, Hungary.