It wasn't just that their symbols looked like swastikas. Or that thousands of Greek flags filled the marble square beneath the Acropolis. Or that they were marking the 560th anniversary of the fall of Constantinople.

It was that there were so many of them. Angry men and angry women furiously screaming "Greece belongs to Greeks" in the heart of ancient Athens, as tourists – some befuddled, some shocked – looked on or fled at the sight of neo-Nazis coming to town.

"Now we are in the thousands," thundered Nikos Michaloliakos, the bespectacled mathematician who leads Greece's far-right Golden Dawn party. "Long live victory!"

Like the soldiers on whom they model themselves, the Greeks who subscribe to the ultra-nationalist, neo-fascist dogma of Golden Dawn are the first to say they are at war. This week, as Antonis Samaras's coalition government struggled to contain an escalating crisis over efforts to curb the extremists, it was they who appeared to be winning that war.

Amid a dramatic surge in attacks on immigrants blamed on the neo-Nazis, the debt-stricken country's ruling alliance has come under unprecedented pressure to crack down on racially motivated crimes. Legislation calling for a ban on parties perceived to incite such violence was proposed by prime minister Samaras's two junior leftist partners last month. Claiming that it would "victimise" Golden Dawn, which has 18 of the 300 MPs in parliament, the conservative groups last week rejected the bill as counterproductive. On Friday they put forward their own, less punitive law.

As parliament prepares to debate how best to apply legislation that will curb the party, – measures that have unexpectedly electrified the political scene – the far right is flourishing in the knowledge that, in a country reeling from the twin ills of austerity and despair, it is they who are in the ascendant. Since elections last year, Golden Dawn's appeal has almost doubled, with successive polls showing support of between 11% and 12% for the neo-fascists. Privately pollsters acknowledge that, as Greece's third-strongest and fastest-growing political force, the group could garner as much as 15% of support in local elections next year.

"It is wrong to believe that they are an ephemeral phenomenon," said Professor Dimitris Kerides, who teaches political science at Athens' Panteion University. "They are not only a product of this country's economic crisis. There is something sick in Greek society that Golden Dawn expresses," he added, referring to the rise in "Greek-only" blood banks and food rallies organised by the extremists. "They are here to stay. And as of 2014 they are going to be everywhere, with access to state resources because, for sure, they will win seats in municipal elections and, in some towns, place mayors."

Emboldened by success, the neo-Nazis have become ever more visible. Across Greece, party branches have been opened at a record pace, with pupils actively recruited in schools. In villages, black-clad supporters proudly sporting the party's insignia have proliferated, and in the southern Peloponnese, traditionally a stronghold of the right, Golden Dawn graffiti are scrawled over the roads and even rocks that dot the landscape of seaside resorts and archaeological sites.

Racially motivated violence has soared to such a degree that European officials blasted Greece for failing to take adequate action. Nils Muižnieks, the European commissioner for human rights, recently felt moved to point out that democracy was at risk in the birthplace of democracy because of "the upsurge in hate crime and a weak state response". It was vital, he said, that domestic and international anti-racism laws were enforced to crack down on violence that had been "linked to members or supporters, including parliamentarians, of the neo-Nazi political party Golden Dawn".

The Greek police and justice systems – both of which have been accused of colluding with the extremists – also had to be reformed, he said.

Indicative of the far right's growing political grip, the conservatives fear that legislation proposed by their leftwing partners will further alienate traditional voters who have migrated to Golden Dawn in disgust at the political establishment blamed for the country's crisis. The party's spectacular rise has been attributed, in part, to defections from the Greek orthodox church and the army.

"The whole thing is a mess," said Dimitris Psarras, an investigative journalist who has followed the group since its incipiency on the collapse of military rule in 1974. "Even if the law is passed, the message that is conveyed is that democracy is divided in knowing what to do with this neo-Nazi threat." For too long, said Psarras, Greeks had watched with complacency as the far-right group went from strength to strength.

Just as in Weimar Germany, when Hitler's National Socialist German Workers' party rose from obscurity, opponents have remained eerily quiet. Until last week, when the 92-year-old poet Nanos Valaoritis deplored Golden Dawn as "having all the characteristics of the party which led Germany to destruction", few in Greece's political or intellectual elite had been willing to take on the extremists.

The lack of public debate has added to the mystique of an organisation whose workings remain opaque. The local media appears to have missed the story of Golden Dawn. To this day, the party's financial backers and advisers remain shrouded in secrecy.

"Few in the establishment have openly addressed the danger of Golden Dawn and almost no one in the media has looked into it," lamented Psarras. "Only now is it being taken seriously, but in my mind that could be too late."

Capitalising on the deep wells of antipathy towards mainstream politicians, the far right has begun targeting the middle class. In recent months Golden Dawn offices have appeared in affluent areas around Athens.

Greece's petit bourgeoisie of shopkeepers and small businessmen has, like civil servants, suffered most from crushing budget cuts demanded by the EU and IMF in return for emergency aid.

In an atmosphere thick with resentment and rage, immigrants from Asia and Africa have made easy scapegoats, with growing numbers of Greeks blaming foreigners for the country's record rate of unemployment – at over 27%, the worst in the eurozone.

"Anger always wants a target," said the prominent clinical psychologist, Dr Iphigenia Macri. "Golden Dawn provides a target, which is immigrants. It is targeting all that anger and sense of abuse that, collectively, Greek people feel at the hands of the government and state."

In a bid to keep passions at bay among a population that reached boiling point long ago, the government has desperately tried to convince Greeks that, three years after the onset of their worst crisis in modern times, there is "light at the end of the tunnel". Optimism has been propelled by economic progress.

However, the neo-Nazis' rise defies any notion that all is well. "The victorious party is Golden Dawn," said political commentator Nikos Xydakis. "Real life is very removed from the success story the government is selling. The neo-Nazis have succeeded not only in demystifying brutality; they are a reflection of the fear and poverty in this country."