Greece, Europe’s most indebted country, has a new government, whose main agenda is the rejection of the repayment terms of that debt. But the two parties making up its parliamentary majority agree on so little, other than refusing the current debt repayment, that Greeks may find themselves going back to the polls soon, after a likely collapse of the alliance between left-wing Syriza and arch-conservative Independent Greeks.

Syriza, the Greek acronym for Grouping of the Radical Left, is a rainbow coalition that, true to its name, runs from former Socialists to unreconstructed Communists. Led by 40-year old civil engineer Alexis Tsipras, who as of Monday is Greece’s prime minister, it has risen to become the standard-bearer of the European leftist parties that refuse the austerity cuts imposed by the European Union as a way out of the fiscal crisis.  

The Independent Greeks, or ANEL in the Greek acronym, are at the very opposite of the political spectrum, a nationalist, rightist movement with a social agenda that couldn’t be further from the secular, progressive Syriza.

Their alliance is born of a common refusal of further public spending cuts to finance the repayment of the 240 billion euro ($270 billion) bailout Greece got in the past five years from the so-called troika of the European Union, European Central Bank and International Monetary Fund. It may even form a template for unlikely political alliances in the two other large EU nations, Italy and Spain, where debt is high and financial austerity is fueling populist resentment.  

But their union of convenience -- Syriza won 149 seats in Sunday’s election out of 300 in parliament, ANEL adds its 13 to get over the hump for a majority -- is built on nothing else.   

“It is very difficult to see how such a heterogeneous coalition would survive beyond a period of a few months,” said Roman Gerodimos, a professor at Bournemouth University in the UK and a specialist on Greek politics.

Tsipras and ANEL leader Panos Kammenos will have to tackle a public debt at 175 percent of gross domestic product, the highest level in the European Union. Financial markets are betting that they will not do so by exiting the euro: the common currency rose Monday against the dollar for the first time in three days, signaling that a “Grexit” is considered unlikely.

“In terms of social issues, foreign affairs, civil liberties, we are chalk and cheese,” Yanis Varoufakis, an economist and Syriza lawmaker, told Bloomberg Television. He is considered among the possible names for finance minister. “What we are hoping for is that the number one issue that concerns the nation and Europe at the moment is one where the Independent Greeks are going to, if not be fully supportive of our stance, at least they will not undermine it,” he said, referring to the debt repayment.

Kammenos also said the “odious” part of Greece’s debt should be written down, even if creditors, Germany chief among them, disagree. That’s an even more radical take on it than some of the statements from Tsipras, who took a more conciliatory tone in the final days of the campaign.

The two may find that they disagree sharply on how to spend any funds saved by negotiating a more lenient debt repayment.

ANEL opposes immigration, a trait it shares with a lot of Europe’s right wing, while Syriza is in favor of a multicultural society. The Independent Greeks also favor a greater role for the Greek Orthodox Church in education, something that Syriza secularists, led by a man who’s been widely described in the press as an atheist, will hardly stomach. Kammenos is also prone to embarrassing conspiracist statements. In December, he said, according to a report in the London-based Daily Telegraph, that Jews paid fewer taxes.

ANEL “has a track record of xenophobic, homophobic and anti-immigrant policies, whereas, for example, Syriza has traditionally supported a separation of church and state, civil partnerships for same-sex couples and giving second-generation migrants Greek citizenship,” Gerodimos wrote in an email.

That isn’t a problem today for the many admirers Tsipras has won among Southern Europeans fed up with tightening government budgets amid a recession. Pablo Iglesias, the leader of Spain’s Podemos or “We Can,” a newborn movement that shot to up to 30 percent in the polls by opposing austerity, appeared onstage with him at the final campaign rally in Athens. He insisted that Syriza and Podemos are the vanguard of a rejection of austerity.

In Italy, Euroskeptics rejoiced. Northern League leader Matteo Salvini, who wants Italy to leave the euro and bar immigrants from entry, said the Syriza victory was “a big slap to the European Soviet Union” -- a reaction that illustrates how the leftist Tsipras has won admirers among leaders who are very far from him on the ideological spectrum.

“At the moment the traditional ideological differences between left and right populist parties are not as important as their rejection of the status quo across the EU,” Gerodimos said, “and therefore we may see other cases of such coalitions or the rise of populist parties that don't have a very clear ideological agenda.”

One of the unlikeliest fans Tsipras has won in Europe is Marine Le Pen, the far-right leader of France’s Front National party and a woman who wants France to reintroduce the death penalty for terrorists. Le Pen, a figure of near-universal reprobation in the European mainstream, made waves when she announced “she would welcome a Syriza victory in Greek elections, if that would further weaken Europe's economic policies,” said Yulie Foka-Kavalieraki, a Ph.D. candidate at the University of Athens and co-founder of What happened next may shed light on what may be in store for Europe’s political future: “Syriza reacted with disgust to the statement. However, today it chose a partner with views very similar to the ones advocated by the Front National.”