Trouble ahead? Europe winces as Greece fails to find a president.

The resulting snap election could see a win by the far-left Syriza party. Many worry its anti-austerity stance could set off a fresh eurozone crisis.

A failure by the Greek parliament to elect a president today not only thrusts Greece into economic uncertainty but could spell the beginning of fresh political woes for the European Union.

Greece had neared the end of 2014 on a relatively high note, with a return to growth. Though fragile, the news of recovery ended one of the longest recessions in post-war Europe.

But the Mediterranean nation now starts the new year facing parliamentary elections that could ultimately see the far-left Syriza win the most votes, according to polls. Syriza openly opposes the strict austerity rules that govern Greece’s current international bailout program – bringing larger worries that Europe could return to the suspense of 2012 when the prospect of a “Grexit” put the bloc’s economic viability to the test.

Yet the political legitimacy of the EU may be most at stake, as populist or extremist parties continue to attract mainstream voters into their folds.

“If Syriza wins in Greece, it might have a multiplying effect in a sense, from Podemos in Spain or the Five Star Movement in Italy to the National Front in France” says Takis Pappas, author of the new book “Populism and Crisis Politics in Greece.” “I don’t think the threat posed by Greece is economic [today], but it is political.”

Greek lawmakers held today the third of three parliamentary votes this month to attempt to elect a president and avert snap elections. But the sole candidate, Stavros Dimas, a former European Commissioner, failed to win the necessary 180 votes.

Antonis Samaras, the prime minister, had warned that a failure to elect Mr. Dimas could mean the end of stability in Greece, which has been in recession for six years. In November, the Greek statistics office showed that GDP had risen in the third quarter by 1.7 percent compared to a year earlier, figures that were unexpectedly positive.

Still, for most Greeks, recovery feels far away, and Syriza has tapped into that weariness.  "With the will of our people, in a few days bailouts tied to austerity will be a thing of the past," Syriza leader Alexis Tsipras said after the vote. "The future has already begun."

Opinion polls have showed that his party would be the winner if elections were held today, with Mr. Samaras’s New Democracy coming in second. In any case, Mr. Pappas says that Greeks should expect more political turbulence and polarization, which threatens to undermine the legitimacy of any new government.

“Greeks are between a rock and a hard place,” says Pappas. “The rock is the very tough austerity measures that have been applied in the last five years. The hard place is the non-existing alternative to that.”

While Syriza scores first in polls, their lead has narrowed. Tsipras has said he aims to keep Greece in the eurozone but that he’d want to renegotiate the terms of Greece’s bailout agreements. And he’s called for a more expansive fiscal policy that Europeans are watching closely.

"The upcoming elections will not change Greek debt. Every new government needs to fulfill the contractual agreements of its predecessors," German Finance Minister Wolfgang Schäuble said over the weekend. “If Greece chooses another direction, it will result in a difficult situation.”

But if this means more political and economic turbulence in Greece, it could also translate into a difficult new direction for Brussels. Mainstream European parties were first shocked in May, when EU parliamentary elections saw populists parties win the top slots in many countries, from the United Kingdom to France.

Le Figaro's editorial on Monday warned about the example that Greece could set for other European countries. “In all of the European Union, the austerity advocated by Brussels and Berlin benefits euro-skeptic parties,” the paper writes. “If it has been justified economically, it has become politically unsellable.”