There is a beautiful scene in the last Costa Gavras movie, Capital. At a family dinner, the chief executive of a large French bank gets into a quarrel with his uncle, a 1968 leftist, who accuses his nephew of indebting European citizens and destroying countries. The young banker answers: “But you should be glad.” The perplexed uncle asks: “Why?” “Because I’m fulfilling your childhood dreams.” “My childhood dreams?” “You lefties wanted internationalism, we’ve got it. Money knows no borders.” However, it seems that global finance might be on the verge of losing this freedom and facing some borders soon – at least if we are to believe the latest polls from Spain, Greece and Slovenia.

They show that Podemos is now the leading party in Spain. The newest of the new left parties in Europe didn’t even exist nine months ago, but if general elections were held today it would get a 27% vote.

In Greece Syriza is the most popular party, with an 11% lead over New Democracy, the liberal-conservative party in the governing coalition. If an early general election were held in February, there is almost no doubt that Syriza would finally be able to form a government.

And in Slovenia the United Left (Združena levica) is the third most popular party. Like Podemos, it was founded only a few months before the last European elections and has the support of other left parties in Europe such as Syriza.

Although these polls raise hopes for a much-needed change in European politics, all these left parties face at least two serious challenges in order to retain mass support.

The first could be summed up as the question of organisation. Although all of them emerged from the protest movements (15-M in Spain, Syntagma Square in Greece), their growing popularity largely rests on charismatic leaders – Alexis Tsipras (Syriza), Pablo Iglesias (Podemos) and Luka Mesec (Združena Levica). Although the motto of the horizontal protest movements was “this revolution won’t have a face”, it is precisely a recognisable face that served as a tailwind for the success of the new left parties. The challenge they now face is how to bridge the gap between horizontality (“direct democracy”) and verticality (“party politics”); how to overcome this traditional problem of all left politics and put in practice – in the context of representative democracy – the principle of “radical democracy”?

It is not for the first time that the left finds itself at this dangerous crossroads. It is what the German student leader Rudi Dutschke back in 1967 called the “long march through the institutions” – which resulted in the founding of the German Green party 13 years later. Does it come as a surprise that it is precisely Joschka Fischer, one of the leaders of the Greens and a ’68 lefty, who now considers Tsipras very dangerous as he is “likely to turn other countries on to dangerous leftist roads” that “would be fatal for the EU”?

The second big challenge is the question of the state. The closer left parties come to power, the more accusations we hear that they are not radical enough any more. The greater the possibility that they could form new governments, the more they are accused of being “social democrats”. It seems social democracy has become the big bad wolf again.

The new left parties are faced with the following contradiction: although they are well aware that the welfare state was the result of a historic compromise between labour and capital, they are forced to fight for the welfare state because it is the last shield in defence of the healthcare system, education, pensions, social security. So the question is: how to avoid the mistakes of the German Greens or the British third way? How to keep the best of the welfare state and not again fall into the trap of strengthening capitalism?

If the predictions that Syriza will be the first truly leftwing government in Europe are realised next year, a test of its success might be found by reimagining that scene in Capital, with a conversation between Fischer and Tsipras. When the ’68 lefty accuses the Greek leader of “turning other countries on to dangerous leftist roads”, couldn’t we imagine Tsipras answering: “But you should be glad.” When the perplexed Fischer responds “Why?”, Tsipras would simply answer: “Because I’m fulfilling your childhood dreams.”