On Monday, Greek lawmakers failed to elect a president in a third and final parliamentary vote that dissolves the current government and sets up snap elections in late January. The outcome, while not unexpected, has reignited worries that domestic political issues in Europe could set off a larger crisis and pose a major risk to the global economy.

The greatest fear is that the weak European economy, which is teetering on the edge of another recession, will cause a backlash among domestic voters and lead extreme parties to major political victories. Last May, such parties across Europe gained seats in European parliamentary elections. In France, the anti-euro National Front party won the national vote for the first time. The U.K. Independence Party topped polls in the United Kingdom as well. And in Greece, the far-left Syriza party came in first with 27 percent of the vote.

Those votes weren't that meaningful since the center-right and center-left blocs still retained enough members to form a governing coalition. But if the extreme political parties took control of government in individual Eurozone countries, it could pose a major risk to the entire European project—and that’s exactly what could happen in Greece with Syriza next year.

“The thing I worry most about isn’t so much Greece but whether what’s happening in Greece affects the politics in the rest of Europe,” said Mark Zandi, the chief economist at Moody’s. “If what’s happening in Greece is a catalyst for broader political change around Europe, I think that’s the real issue.”

The political unrest in Greece stems from the country's dire economy. More than six years after the financial crisis, unemployment is above 25 percent, and youth unemployment is far higher. Economic growth is below 1 percent and inflation is negative. Deflation, as it is known, makes it harder for debtors to deleverage and pay off their debts. Businesses and consumers hold off spending money under the belief that their money will be worth more in the future. Less consumption means fewer jobs, which causes businesses and consumers to further reduce their spending. This entire cycle repeats itself.

This has all been made worse by the European Commission and European Central Bank (ECB) which have demanded strict austerity measures from the government in exchange for financial support to Greece so it can avoid a default. Those measures have come in the form of pension cuts, spending cuts and tax increases—leaving Greek citizens with less money to spend and exacerbating economic problems.

Under those conditions, you can understand why fringe political parties have gained traction in Greece. Syriza, in particular, has earned significant support under a campaign to renegotiate the conditions from the European Commission and ECB. If Syriza does win the elections in January and earns enough votes to govern—and that's a major “if”—it’s hard to predict what will happen next. The ECB and European Commission could reduce their demands and reach a new compromise with Greece, with the understanding that a Greek default and subsequent exit from the Eurozone—the so-called Grexit—would have disastrous consequences on all of Europe and the global economy. The risks for the Eurozone are much higher if support for extreme political parties in other Eurozone nations continues to grow.

“[Syriza] obviously doesn’t like the austerity so they’ll push back on that but I think they’ll find some middle ground, some compromise,” Zandi said. “Short of leaving the Eurozone, I don’t think that’s what anybody in Greece wants including this breakaway party.”

Yet markets are nervous. Germany has an outsized influence at both the ECB and European Commission, and is determined to use its financial leverage to force Greece to make structural changes to its economy. If Germany becomes determined to hold a hard-line negotiations with the Syriza-run Greek government, the odds of a "Grexit" could rise substantially. Already on Monday, yields on 10-year Greek bonds rose nearly 1 percentage point, to 9.7 percent. That could provoke similar fears in other periphery nations in the Eurozone.

That is all months off. Greek attitudes toward Syriza may shift if the party's chance of gaining control of the government increases. There may be another political stalemate with parties unable to form a governing coalition. But the risks are real—not just for Europe's economy, but the world's.