Cologne is known as one of Germany’s most open and tolerant. When the anti-Islam group Pegida staged a march here at this time last year, the city's iconic Gothic cathedral famously rejected their message by dimming its lights.

But a year later, the cathedral was the backdrop for a New Year’s Eve mob that saw more than 120 women taunted and groped or robbed by men described as foreign in appearance – an incident that is testing the limits of German tolerance and could ultimately force the country to take new, uncomfortable stands on the migration crisis in Europe.

The events of New Year’s Eve are murky. Only 30 suspects have been identified out of a reported crowd of 1,000 who police say surrounded women in smaller groups around the cathedral and main train station, sexually assaulting them throughout the evening. No official motive has been given, nor an explanation offered into how or even if the attacks were organized.

But police described the suspects as “Arab or North African,” and the government confirmed today that half of them so far are asylum seekers. That has ignited a charged debate about whether Germany, whose Chancellor Angela Merkel has been lauded for her moral leadership, can manage to accommodate the hundreds of thousands who have been let in.

Many Germans are now saying that the Cologne incident has crystallized the sense that the country must engage the consequences of the large and sudden flow of immigrants more directly, warts and all. They say that the confluence of failures – media that downplayed the evening's horror, police accused of covering it up, and a political culture that has not vigorously debated mass migration for fear of stoking the far-right – shows that Germany needs more honest assessments of the crisis.

“We are in a dilemma. We still want to welcome people,” says Holger Geissler, of the polling firm YouGov in Cologne, "but this is a very clear signal that we have to take the whole refugee situation more seriously than we have.”

'The police didn't do anything'

The police have so far faced the harshest spotlight, with police chief Wolfgang Albers being suspended today. Many are asking why they failed to stop the violence, only arresting a handful of suspects and leaving women feeling vulnerable.

Even worse, they did not initially report it. At 8:57 a.m. on Jan. 1, in fact, the police issued a statement saying that the evening was peaceful. Only as women started publicly reporting the incidents did they backtrack.

Later in the week, German media reported on internal police documents showing that cops knew asylum seekers were among suspects. Kölner Stadt-Anzeiger, a Cologne newspaper, quoted anonymous police sources who said the officer leading the investigation declined to mention it in his report fearing that it would be “politically awkward.”

But such positions are now under attack. The conservative daily Frankfurter Allgemeine wrote that “When such lawlessness takes over in ... Cologne’s showcase place, then politicians, police and the courts can no longer look away.”

Leili Shabani, a recent refugee from Iran who was one of thousands in the crowd on New Year's Eve, agrees – even if the consequences directly affect her.

She was eager to join her husband and a group of friends, half of them new refugees, outside the cathedral. “It was my first New Year’s Eve here, I wanted to see what it was like,” she says. But around 11 p.m., chaos ensued as men started swarming through the crowd, stealing firecrackers and setting them off, she says, and intimidating and terrifying women around her.

She shows an injury on her hand from a firecracker that hit her as she attempted to protect her three-year-old in a stroller. When, in her native Farsi, she asked the three men who crowded around her group what they were doing, she says they answered her in Arabic.

“The police didn’t do anything,” she says. And while she fears the incident will darken the mood against refugees, she says it needs to be faced. “If I was German I would lose my trust in foreigners, too,” says Ms. Shabani.

Muted media and overwhelmed authorities

As Cologne’s famed Carnival celebrations near next month, the police have announced plans for more surveillance and staff. "The police need to be in greater numbers in these areas,” says Alexander Bosch, a consultant for "hate crimes" and "police and human rights" at Amnesty International in Berlin.

An internal police memo obtained by the German press described a night in which perpetrators acted with impunity because the local police force simply couldn’t handle them.

Peter Pauls, editor-in-chief of the Kölner Stadt-Anzeiger, has been documenting lawlessness in the plaza, including claims of sexual assault, for years. On New Year’s Eve, one of his photographers had his equipment stolen at the station. “When he tried to gather the police, he was told to get in line,” says Mr. Pauls, who added that at the time, the photographer could still see the suspect with the equipment in his hand. “The police were clearly overwhelmed.”

The media have also come in for intense criticism.

After initially reporting that all had gone well, based on the first police report, the Kölner Stadt-Anzeiger covered the growing claims of a disturbing night. But Lutz Frühbrodt, a professor of journalism at Würzburg-Schweinfurt University, says the mainstream media ignored it for days. While some of that is government influence on the media, he also sees an innate media instinct that has its roots in the 1920s, when the press was condemned for not doing anything to counter the rise of Adolf Hitler.

“The major problem for many established media like the national dailies, the bigger regional papers, and public TV is that they struggle with a trade-off between social responsibility and independent, impartial reporting,” he says. “I think most of these media have had a bias toward social responsibility … preventing racism and promoting the German ‘welcome culture,’ ” or Willkommenskultur.

The press has since acknowledged mistakes. The broadcaster ZDF publicly apologized for not including Cologne as a news item on its Monday night program, calling it a “misjudgment.”

A punitive position

Authorities have long been at pains to reassure the public that having more refugees does not mean more violence. But the conversation has changed, and Germany's overall approach to policing refugees might see some big changes in the wake of New Year's Eve.

Many politicians are now calling for tougher penalties against asylum seekers, including an easier vehicle for deportation. Mrs. Merkel seemed to be receptive to the idea this week. “We’ll need to examine whether we’ve done everything that’s needed in terms of expulsions from Germany, so we send a clear signal to those who aren’t willing to obey our legal standards,” she said Thursday.

Vice Chancellor Sigmar Gabriel, of the Social Democrats with whom Merkel governs in a coalition, reiterated that point today. "Why should German taxpayers pay to imprison foreign criminals?" Mr. Gabriel asked. "The threat of having to spend time behind bars in their home country is far more of a deterrent than a prison sentence in Germany."

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This dialogue places Germany in uncomfortable territory, says Joachim Kersten, a professor at the German Police University in Muenster. “This has hit the German nerve, the nerve of trying to be ‘good Germans,’ ” he says. “In a situation where people behave like that … you have to apply laws of a democratic society. When things get that bad, you have to come to grips that we are now in position that we don’t like: … to be punitive, to apply sanctions.”

But that could ultimately save the Willkommenskultur that was born in the volunteerism along the tracks in the Munich train station from withering on the steps of the station in Cologne.