"Das Titanic Szenario" was the headline on Friday on the front page of Handelsblatt, one of Germany's most-respected business newspapers. Inside, Angela Merkel was pictured, arms outstretched, on the bow of the sinking ship, with Nicolas Sarkozy in the Leonardo DiCaprio role embracing her from behind. Days earlier Jacques Delors, a former president of the European Commission, had said the eurozone was "on the brink of the abyss".

There was similar doom-mongering in Der Spiegel. "The euro can't survive in its current form," proclaimed Hans-Joachim Voth, an eminent economic history professor from the Universitat Pompeu Fabra in Barcelona. Some countries were going to have to leave "if [the EU] wants to become anything more than just a transfer union", he said, adding that "it would be simpler to have the stronger countries veer off". And which of the 17 eurozone nations did he have in mind? Deutschland.

But could Germany seriously leave the euro? Is the common currency on the verge of collapse? "It's not looking good," said Jane Dill, a 20-year-old logistics student on a college outing to the Money Museum of the Bundesbank, Germany's National Bank, in Frankfurt. "How much longer can things go on like this? First Greece asks for help, then Portugal, Ireland, maybe Spain and Italy. What are we going to do when the next countries fail? You can't just keep chucking money at them. And what if Germany needs help? Who will come to our aid?"

"Even the rouble's more reliable," said her classmate, Edward Krieger, a 24-year-old with an even gloomier Weltanschauung. "I honestly believe the euro has no future. It's going to crash and a whole new currency is going to have to be brought in. Maybe money as we know it will be abolished. I think in 20 years' time there will be one currency used by everyone in the world."

In the gift shop at the foot of the European Central Bank (ECB) tower, Gebhard Klotz was more optimistic. "Will the euro collapse? No!" scoffed the 64-year-old shop assistant as he tidied the display of chocolate money. "The euro will survive. Of course it will. Unity costs money, that's all. It's just the way it is."

In his office 34 floors up, Jean-Claude Trichet, president of the ECB, would share this optimism. "Weaknesses need to be corrected," he conceded in an interview with Il Sole 24 Ore last week. But the single currency was "credible" and "over the past 12 years has kept its value in terms of price stability in a remarkable way in comparison with the previous national currencies in the past 50 years".

Much has been written about German nostalgia for the deutschmark; last December some stalls at the Christmas market in Berlin's Gendarmenmarkt let punters pay with the old currency in what proved to be a very popular marketing gimmick. Around the same time, a survey by Cologne's YouGov-Institute found that 49% of Germans want the "D-mark" back.

However, if Klotz's customers are anything to go by, the longing is not widespread in Frankfurt. His shop sells two ranges of mugs, one plastered with euro notes, another, also priced at €6.90, depicting the deutschmark.

"The euro is much more popular," said Klotz's colleague, a 23-year-old coin enthusiast called Florian Koch. "We sell 30 or 40 of them every day."

Both men were adamant they would not soon be made redundant or the shop reborn as a shrine to what once was. "Yes, the euro is sick," said Koch, a business student at Frankfurt University, "but it's healthier than many other currencies. It's limping at the moment, but it's not going to go kaput."

This week is a big one for the euro in Germany. On Wednesday, the constitutional court in Karlsruhe will deliver its eagerly awaited verdict in three cases brought by five eurosceptic academics and a renegade MP from the Christian Socialist Union, the Bavarian sister party to Merkel's Christian Democratic Union. The plaintiffs argue that last year's bailout of Greece, Ireland and Portugal was illegal because it was not debated in the Bundestag, Germany's parliament.

Merkel spent yesterday mourning the death of her father on Friday. This Thursday she must quell a threatened revolt in her own parliamentary bloc when the Bundestag begins debating the controversial expansion of the rescue fund, which increases Germany's share of guarantees to up to €211bn (£184bn) from a previous €123bn – about two-thirds of the annual federal budget. MPs will vote on the changes on 29 September. And Friday is the deadline for private-sector participation in a second Greek rescue package, Merkel having asked the commercial world to voluntarily chip in after resolutely failing in a bid to force them to do so. News that Greece is set to miss its latest financial targets will not have bolstered confidence.

As Europe's largest economy, Germany foots more than a quarter of the bill for eurozone bailouts. Much of that money stems from Frankfurt am Main, the birthplace of Goethe, a surprisingly small city affectionately referred to as a "village of skyscrapers". Despite only being Germany's fifth-largest metropolis, with a population of just over 688,000, it is the financial capital of not just Germany but also the eurozone.

Frankfurt's stock exchange, the Deutsche Börse, is more of a tourist attraction than a trading hall in these unromantic days when all you need to trade is a powerful computer and a strong disposition. But the neo-Renaissance sandstone building remains at the heart of the financial district.

Every Friday lunchtime, suited and booted bankers ring in the weekend with a glass of local wine or beer at the weekly farmers' market, which sets up outside the exchange by the famous Bear and Bull sculpture, which is a metaphor for the rise and fall of the Dax, Germany's equivalent of the FTSE.

It did not feel pessimistic last week. Harald Feick had lined up three glasses of wine. "Two friends are coming! They are not all for me!" he insisted, and explained why he has no fear for Europe's common currency. Describing himself as "ein bankmensch", he said the crisis was "not about the euro; it's about financial mismanagement in certain European governments. The Greeks would be in the same trouble if they still had the drachma."

The German media was too pessimistic, he reckoned. "You hear all the gloom, but a lot less about the fact that, despite the crisis, we have decreasing unemployment and an economy that is growing, albeit slowly." Quarterly economic growth slowed to 0.1% in April-June.

Robert Hung, a blond banking lawyer in a crisp white shirt and dark suit, said the tabloid media – in particular the three million-selling Bild – was partly to blame for a feeling of discontent among the general population, spreading the overly simplistic idea that money earned by hard-working, prudent Germans was being frittered away by profligate Mediterraneans.

Hung, 36, and his heavily pregnant wife, Fabienne, said they had been on holiday to Greece this summer and were "embarrassed" at the reputation Germans had on Crete. "When the receptionist saw our passports, he said, 'Please, when you go home, tell everyone that not all Greeks are lazy. Tell them that many of us work very hard'," said Fabienne. "It was embarrassing."

Hung admits he is having a good crisis – he has been inundated with cases from banks defending themselves from crash-related lawsuits – but not everyone is a winner.

"We can't rescue everyone," said Barbara Schiml, enjoying a wine in the sunshine with her husband, Udo. "The government needs to set boundaries. We can't keep bailing out other countries for ever." The couple agreed it should be harder for other countries to join the common currency in future.

Antonia Gugel and her friend Elisabeth Brändl, both in their 80s, are typical of a generation which grew up treasuring the deutschmark. They are, to put it mildly, disapproving of the current mess. "When we started work after the war, there was nothing. Germany was in ruins. We had to build up everything ourselves," said Gugel.

"We worked Monday to Saturday, had 12 days' holiday a year and didn't spend what we didn't have. Young people today have grown up in prosperity. If they want something, they put it on their credit cards. They have never had to learn the value of money. That's at the root of all these problems."

• This article was amended on 5 September 2011. The original referred to Frankfurt am Rhein. This has been corrected.