The country responded generously as Angela Merkel threw open the borders, but as 1,000 people a day arrive in the capital alone some doubts are being voiced

The Rudolf Harbig hall in west Berlin is normally used for athletics. The complex has a track, an indoor sandpit for long jump and a gallery for spectators. Nearby is the monumental Olympic stadium, the scene of the 2006 World Cup final and other major sporting events.

On Friday, however, the hall was being transformed into emergency accommodation for refugees, now arriving in the German capital at the astonishing rate of 1,000 a day. Soldiers from the German army were unloading mattresses. New camp beds had arrived. Some 15 volunteers were busy stuffing colourful covers on duvets.

“We’re sacrificing our gold medal to help people in need,” said Thomas Glückselig, lugging a mound of bedding. “Great Britain will get the gold instead of us,” he joked. Glückselig, a 60-year-old Berlin pensioner, said Germany had no choice but to shelter all of those fleeing war. But could the country manage? “If we can save banks, we can save people. We want to do it and we can do it,” he replied. What about other EU countries, such as Britain and the east Europeans, whose leaders appeared less keen on refugees than Angela Merkel? “If England wants to be in Europe, you have to do more. You can’t shut your tunnel,” he said.

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There are currently more than 250,000 unprocessed asylum applications. Germany’s much-criticised migration ministry says it is urgently recruiting extra staff. It wants to reduce the waiting time for an asylum decision from at least five months to three. Other professionals also have to be hired: language teachers, classroom assistants, psychologists. Berlin’s multi-ethnic Neuköln district offers 13 different German courses for beginners. All are full.

Germany has an ageing population and one of the lowest birthrates in the world. Its industry has cautiously welcomed the refugees, seeing them as a potential boon. But it is unclear how long it might take to absorb them into the workforce. Only one in 10 is immediately employable, Berlin says; the rest will require social support for months, possibly years, to come. Merkel has stressed the importance of education. Last week she visited a Berlin school where refugee children were learning with other kids in a so-called “welcome class”. Politicians on the left and right are keen to avoid mistakes made during the country’s last great wave of immigration – from Turkey in the 1960s and 1970s.

Merkel has insisted that Germany can cope with its biggest logistical challenge since reunification a quarter of a century ago. “Wir schaffen das!” the chancellor said optimistically 13 days ago – we can do it! Germany was a “strong country”, she argued. Undoubtedly Germans have taken her message to heart, giving money, clothes, food and offering their spare rooms.

Facebook Twitter Pinterest Angela Merkel posing for a selfie. Photograph: Sean Gallup/Getty Images

Melanie Stannek, another volunteer, said the plight of the refugees touched everybody. Her parents had been refugees too, she said, fleeing as small children from Silesia – now in Poland – during the second world war. “The system works for now,” she said, taking a pillow case out of its plastic wrapper. She admitted, however: “I’m not sure about next week.” “We’re trying to make things cosy,” Claudia Brückner added.

Despite the heart-warming scenes at Munich railway station, where refugees have been met with applause, there are growing doubts about Germany’s capacity to deal with this influx. The numbers are extraordinary. In August, 160,000 refugees came to Germany. The figure for September stands at 60,000. This weekend 40,000 are due to arrive in Munich from Austria.

By the end of 2015, Germany expects at least 800,000 asylum applications. The figure, Berlin admits, could reach 1 million.

For the moment, the priority is managing this endless human tide. With Bavaria unable to cope on its own, refugees are being shared out among Germany’s 16 regions. A computer system, Easy, calculates how many people each region should take. It uses a “Königstein formula”, which weighs population and relative wealth. Special trains from Munich then dispatch refugees to towns and cities.

Under this formula, Berlin is obliged to take 5% of all new arrivals. The city government has been scrambling to find accommodation. Two weeks ago it turned over a police barracks in Berlin Spandau. Two sports halls, including Rudolf Harbig, have been commandeered. The government is now discussing using Tempelhof airport, which shut down in 2008 and was the scene of the 1948-49 Berlin airlift.

Other venues under consideration include a velodrome in the Prenzlauer Berg district and empty hangars in the defunct trade fair building. In Frankfurt an der Oder, in neighbouring Brandenburg, refugees are staying in a hotel. In nearby Eisenhüttenstadt they are living in converted barracks in the middle of a pine forest.

On Thursday, 500 refugees moved into another sports hall, next door to the athletics complex. Its giant playing area for handball and volleyball is now decked out with campbeds. Women sleep on the left; men on the right. Outside, children were playing football; one was doing a donated jigsaw puzzle; groups of young men sat around charging points for mobile phones, munching on bread and cheese.

Facebook Twitter Pinterest Aerial view of a provisory tent village for refugees and migrants in Eisenhuettenstadt. Photograph: Patrick Pleul/AP

Ahmad Khalit, 18, from Kabul, said he had fled from Afghanistan after the Taliban killed his parents. The journey took six months. He had washed dishes in Turkey, crossed to Greece in a wobbly boat, and spent 15 days sleeping rough. Hungarian police arrested him; in jail he got a breadroll every 24 hours. “I’m psychologically and physically exhausted,” he said. What now? “I’d like to proceed with my education.”

Most of those arriving in Germany have an overwhelming case for asylum, but the country’s regions say they are close to collapse. Merkel’s coalition government has promised the Länder an extra ¤3bn (£2.2bn). The regions say that this isn’t enough. On Thursday, regional interior ministers held a mutinous conference call with their federal boss, Thomas de Maizière. They told him that, unless Berlin made army barracks available, Germany would have to shut its borders.

Criticism of Merkel’s decision to allow unregistered refugees to enter the country has been growing. The Bavarian CSU, sister party to Merkel’s CDU, is scathing. “This is a mistake that will occupy us for a long time to come,” CSU leader Horst Seehofer told Der Spiegel. He added: “I don’t see any way of putting the stopper back in the bottle.” Another CSU politician, Hans-Peter Friedrich, called it “an unparalleled political mistake”.

With eastern Europe refusing to take part in a refugee quota system, set out last week by European commission president Jean-Claude Juncker, some inside the CDU are also having doubts. On Thursday, Merkel visited a Berlin reception centre. Refugees took selfies with the chancellor. “When these pictures go round the world, everyone will know they can come to Germany,” one CDU man told Der Tagesspiegel.

Others from Merkel’s party have been supportive. Martin Patzelt, a CDU MP, attracted national headlines after temporarily taking in two refugees from Eritrea at his home in Brandenburg. He told the Observer that Germany could cope, but admitted there was “definitely a risk” that the influx would drive voters into the arms of the far right.

Germany has seen attacks on asylum seekers’ hostels as well as regular, if sparsely attended, protests by radical activists. Last month neo-Nazis attacked a refugee home in Heidenau, near Dresden, battling police for two successive nights. Patzelt has received death threats on his answering machine. The solution was a sustained and dedicated push from civil society, he said.

Facebook Twitter Pinterest Refugees are accompanied to an asylum-seekers’ accommodation after their arrival in Munich. Photograph: Sven Hoppe/AP

On 18 September, Merkel celebrates a decade as chancellor. She is Europe’s leading politician and the most influential woman in the western world. Yet there is a sense that refugees – for better or worse – will become the defining issue of her chancellorship, and one that affects her chances of re-election in 2017. She has German public opinion on her side. But for how much longer?

For those who have made it to Germany, Merkel is not just a saviour but a figure from myth. Douaa Saba, 18, and her father, Waad, fled from Mosul in northern Iraq. They are now living in the Schmidt-Knobelsdorf barracks in Berlin Spandau, with 1,600 other refugees. “Merkel is a good woman. We will tell our children stories about her. They will tell their children,” she said.

Douaa speaks fluent English, learned Turkish while living in a camp, and wants to be a pharmacist. She described Islamic State – who overran Mosul in 2014 – as “monsters”. One senses that she will adapt quickly to Germany. Other refugees, however, appear dazed and traumatised. The camp is already full, the latest arrivals are being housed in rows of white tents in the courtyard.

Bilel Feachichi, 18, said he had come from Misrata in Libya. He and his two tent-mates looked exhausted. The tent was chilly and they only managed a couple of hours’ sleep, he said. Bilel admitted he had no plan. He said he didn’t want to stay in Germany, but would like to go to London or Canada instead.

Back in Olympiastadion, buses were bringing the latest refugees to their new home in the Rudolf Harbig hall. Its indoor long-jump sandpit was fenced off. The stadium has seen many historic moments, including Hitler’s 1936 Olympic Games. The refugees are living down the road from Jesse Owen alley, Berlin’s British school and leafy suburban streets named after English novelists.

“I can’t go back to Afghanistan. There you have two choices: fight for the Taliban or be shot,” said Khalit, the refugee from Kabul. He added: “German people are very nice and very hospitable.”