The early hours of a Monday morning, four days before Christmas: it’s not a time you would expect to see thousands of Spaniards waiting patiently to hear the Ghostbusters theme tune. But then the crowd of people who gathered in the Plaza del Museo Reina Sofía in Madrid in December were Podemos activists who knew that the song would herald the arrival of Pablo Iglesias, the ponytailed leader of the left-wing party. Hours earlier, Iglesias had led Podemos – still less than two years old – to third place in the national elections, breaking more than 40 years of political convention.

The rise of Podemos has paralysed Spain. The party won 69 seats in the Congress of Deputies before Christmas but, more importantly, as Iglesias had promised, it disrupted the two-party system that had dominated since democracy returned after Francisco Franco’s death in 1975.

For eight years, Spain has endured savage austerity measures – a hangover from its profligate bingeing on cheap debt in the 2000s – and flagrant corruption, which has reached the upper echelons of the ruling centre-right People’s Party (PP) and, allegedly, the royal family it supports. Podemos’s pitch to voters was an end to the status quo, a slowing of austerity and an escape from economic policies dictated by Brussels and Berlin. Within days of being elected, the party’s MPs pledged to accept a lower salary than the official rate offered and to do away with many of the perks that come with the job.

As a result of Podemos’s success, neither the PP nor its left-wing opposite, the Spanish Socialist Workers’ Party (PSOE), managed to win outright. The governing PP won 123 seats, down 64, while the PSOE won 90, with neither coming close to the 176 seats required for a majority.

Forming coalitions is no simple task. A grand coalition between the PP and the PSOE would be enough to form a government but the PSOE is unlikely to assent. Not only is the party aware just how poorly junior partners fare in grand coalitions – consider Germany’s Social Democrats – but it knows that, by the general election in 2019 or early 2020, it would struggle to claim credit for government successes and be unable to mount an opposition from the left, a position that Podemos would swiftly occupy.

For these reasons (not to mention significant personal animosity), Pedro Sánchez, the leader of the PSOE, appears to have scotched all possibility of joining forces with Prime Minister Mariano Rajoy. Instead, he seems to favour a leftist alliance that would bring Podemos into government.

Yet there are problems here, too. Podemos has promised a binding referendum on Catalan independence: something that is abhorrent to the PSOE. To make matters worse, any coalition would likely need the support of the far-left, pro-secessionist Republican Left of Catalonia (ERC) to get close to 176 seats. Because of all this, as newly elected politicians arrived at parliament during the week, the job of selecting a new prime minister remained incomplete.

Ángel Talavera of Oxford Economics predicts an 80 per cent chance that the parties will find it impossible to form a coalition and Spaniards will be asked to return to the polls. “We still think that any of the alliances required to form a new government is extremely unlikely,” he says.

Rajoy’s pitch to voters was one of economic stewardship, not unlike that of the Tories in Britain last May. Now, the markets are getting jittery. The prime minister has promised to form a strong and stable government but it is difficult to see how. What would another vote change? The economy is getting stronger, which plays into the PP’s hands – as does the way that Citizens, the centrist party that came fourth and is believed to have stolen votes from disillusioned PP supporters, did worse than expected. Analysts predict that PP voters will return next time, having registered their protest.

There is pressure, too, for the PSOE and Sánchez. Despite sitting opposite an unpopular government, the party lost 20 seats. Rumours are already circulating that Sánchez’s leadership may be challenged by Susana Díaz, the PSOE’s premier in its Andalusian stronghold. It could be assumed that the PSOE’s electoral failure would play into Podemos’s hands but Pablo Iglesias’s refusal to abandon his promise of a binding referendum on Catalan independence will deter those for whom unity is important.

It is likely that a series of elections and leadership battles will ultimately produce a government. As Podemos’s Ghostbusters theme tune unwittingly predicted, there’s something strange going on – and nobody knows who they’re gonna call.