To keep tactical voters on their toes, politicians running for office make the chances of power-sharing look slim. Hardly ever do they sound as uncompromising as António Costa: “I would consider a grand coalition in the event of an alien invasion,” Portugal's socialist party (PS) leader, said in an interview.

His remark exposed the catch for the centre-left in the 4 October parliamentary elections. The socialists stand a decent chance to return to power, but with no absolute majority in sight, the party faces an existential question: will it give in to the pro-austerity parties on its right or strike a deal with the die-hard communists to form government?

Back in 2011, it was hard to imagine that PS would manage to walk away from the crisis largely unscathed. In that year, a socialist government turned to the EU for financial assistance and was forced to resign. In Greece and, to a lesser extent, in Spain, protest parties like Syriza and Podemos drained support from the centre-left, as the recession took hold. In Portugal, though, the socialists were back in the lead in opinion polls after just one year in opposition and went on to win the local and European elections – in a ironic twist to the history of the Euro crisis.

Pedro Magalhães, a researcher at the Institute of Social Sciences in Lisbon, argues that one of the reasons for the turnaround was the election of a party leader who was seen as one of the major ‘inner critics’ of the former government. At the same time, the strength of the old Communist Party, behind which the opponents of liberal economic policies and European integration historically rallied, limited the opportunity for the emergence of new political forces.

The crisis has produced an unusual political landscape, nonetheless. Aggregate support for the three mainstream parties is at about 70 per cent - the lowest level since the late 1980s. What is more, voters are unusually split. According to PopStar’s poll of polls, PS and the incumbent right-wing coalition – the centre-right social democrats and the Christian democrats are filing a joint list of candidates – are neck and neck at 36 per cent. The communists come in third with about 10 per cent. The Left Bloc, Syriza’s sister party, has five per cent. Most of the remaining votes are wasted – a consequence of the D’Hondt method.

About one in three voters are still undecided, but it is probably wrong to rely on them to tip the scales. Research shows that voters who make up their minds late do not tend to behave in a radically different manner than those who have stronger political predispositions and decide earlier. The ones that should be a cause for concern are those who claim to have decided how to vote, but do not show up on the day of the election. “As it happened in the last general election in the UK, differential turnout of this sort is a big problem for opinion polls in Portugal,” Magalhães says.

In the early days of the campaign, party leaders insistently targeted their core constituencies. The TV and radio debates between party leaders were focused on differences between plans to phase out the tax hikes imposed under the troika and to plug the social security funding gap. The socialists want to cut taxes faster than the right, to give the economy a boost. They also propose allocating a share of corporate tax to social security funds, as an alternative to cutting pension entitlements.

With less than two weeks until the vote, it is the answers about the electoral maths of the day that draw attentions. ‘Victory’ will be a term hard to define. Even if the socialists come second, they will elect more MPs than any other party. More importantly, with no absolute majority likely, the ability to forge an alliance with other political forces will be the key to form a government and retain power over time.

Costa has gone to great lengths to rule out a grand coalition drastically restricting the number of possible solutions for the looming political deadlock. Pedro Passos Coelho, the current prime minister and leader of the right, has no one left to negotiate with. Even if the right wins, he might not be able to get his programme for government approved in Parliament.

The socialist leader has more options. Costa could hope the right would abstain on key votes or he could turn to the Communist Party for support – the support of the other parties is insufficient. This would be a first. The socialists ruled in coalition with PSD and the Christian-democrats in the 1980s, but never in 40 years of democracy have they shared power with the communists. The last three times the party came ahead in a parliamentary election, but failed to secure a majority, it preferred to form a minority government. The last time this happened was in 2009. Two years later, the communists and the right joined forces to pass a no-confidence motion.

Costa has kept a conciliatory tone towards the far left and reminded voters how, as a mayor of Lisbon, he managed to build a broad coalition. The problem is that the communist proposals for the country – from the Eurozone exit to a much looser tax policy – fly in the face of the socialists’ plans. The party would be tempted to go alone and seek support for its bills on a case-by-case basis. “We cannot reach a compromise with the right, as we oppose austerity and policies that reduce the quality of public services. So long as the political forces to the left of PS want to remain as protest parties, governing alone is an inevitability,” says João Tiago Silveira, a party strategist, who was put in charge of the electoral manifesto.

If this is case, Costa will be vulnerable before the opposition in Parliament. His days in office will probably be numbered. And the country will start bracing itself for a snap election.