Two young men sidle up to Ahmad Majid on Wednesday night. He is standing in the underground concourse of the Keleti train station in Budapest, which the stranded migrants have effectively taken over, spreading out blankets to sleep, playing cards and dandling babies to pass the time. Having been forbidden to board trains leaving Hungary, they are trapped, and Mr. Majid is trying to figure a way out.

The two young men have paid a smuggler to get them over the border to Austria. Mr. Majid gives them a slip of paper with his phone number on it, and they promise to let him know in the morning whether they were successful.

At just over six feet tall, in his bright yellow shirt, Mr. Majid stands out like a skyscraper among the refugees, who are generally much shorter than either him or the Hungarian riot police who are now surrounding the train station. That difference in height appears to be one way for the police to profile the migrants, preventing them from passing beyond the concourse or the station doors to the train platforms.

Mr. Majid does not seem to fear his visibility. He always wears brightly colored shirts, generally orange, yellow or white.

The police are also making periodic sweeps on the surrounding neighborhood, questioning, detaining and fingerprinting people who look like they cannot prove they entered Hungary legally.

As the police carry out their sweeps, more and more of the migrants have been detained and fingerprinted in this manner and now carry registration papers. Some also have small, white identity cards encased in a plastic sleeve. The cards show migrants' first and last name and their citizenship, usually “szir,” for Syrian. (The word “citizenship," written in Magyar, is misspelled.) The cards are also printed with a bar code. The space for a photo is blank.

The cards are their passport in and out of a camp, they say. But will they be able to travel with these documents? They do not know.

The migrants are instructed to report to a refugee camp and are given maps and Metro directions to get there. But many of them ignore the instructions and go instead to the train station, where they feel safer because they feel at least somewhat in command of their own destiny, rather than like dependent children.

The Majid family, who crossed the border illegally, so far have escaped the fingerprinting and identity card process. They stay in the train station not because they want to, but because it seems more dangerous to leave. Over the last eight days, they have traveled overland through Athens, Thessaloniki and Idomeni in Greece; Gevgelija and Tabanovce in Macedonia; Presevo, Belgrade, Kanjiza and Horgos in Serbia; Szeged in Hungary, and now, Budapest.

Budapest seems the most treacherous.

Mr. Majid believes that at this point, the only way he can get his family to Germany and then to relatives in Sweden is through a smuggler. The network is active in the train station encampment. But with the bottleneck in Hungary, prices have escalated prohibitively. Where smugglers once wanted 300 euros, or about $335, a person to travel into Austria, they now want €600 to €1,000 a person. One smuggler has offered Mr. Majid passage for €800 a head, he says, sitting on a blanket where he has been playing cards with three other men and smoking Gauloises. Even if he narrows his family group of 14 people to 10, the cost is still exorbitant.

Another smuggler has offered €600 a person. But that smuggler seeks a quota of 20 people to ride together, so Mr. Majid suspects that they would be riding in a truck. He will not risk putting his pregnant wife and children in one. Every migrant now knows the story of the 71 migrants who suffocated in a truck in Austria.

“It’s just getting harder every day,” Mr. Majid says. “Today I’m thinking we have to find some way to get some money. We will wait a day or two, then get out.”

Time, he says, is against him. Everyone at the train station is afraid the police will finally crack down and force them to move to the official camps.

Mr. Majid has weighed sending a few of his group to the border first, a kind of scouting expedition, the tactic he used when sneaking across the border from Serbia. But he has ruled it out. It would be inequitable, he says, and if there has been one principle of his leadership during this journey, it has been to treat everyone fairly.

“The problem is, we’re all tied together,” he says. “Who do I send first?” He has put the question up to the group, which includes his older brother, Farid, and his brother-in-law, also named Ahmad, for discussion. “Everyone starts to have different thoughts,” he said. “If I send the guys first, I am sacrificing them. If I send Farid, I am favoring him. If I go, I am only thinking of myself. We are all in this together.”

At the border, Mr. Majid had rallied the spirits of his group and insisted on trying again after the police stopped them from crossing the first time they tried. When they finally succeeded in sneaking through, just a few yards from a parked police car, Mr. Majid waited until everyone else had crossed before crossing himself.

“I was the last one out,” he recalled. “I couldn’t cross until everyone else went through. If I hadn’t pushed it, putting up the ladder, trying a different spot, they wouldn’t have gone through. All that effort would have been for nothing.

Everyone has entrusted me with their family members.”

“Ahmad is the son of my father-in-law, my wife’s brother. Someone else is the son of my uncle. So I have no choice because I will be held responsible for them.”

The sense of responsibility was mutual, he said.

“They were saying, if you don’t go, we won’t go," he said. "So is it really logical for me to leave them now and go on my way? There’s no way.”