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Like the Tea Party movement in the U.S., whose clashes with the political mainstream caused a government shutdown last year, the rise of right-wing, anti-big government parties on this side of the Atlantic could threaten the work of the European Union (EU) and the wider international community, experts and politicians told CNBC.

As the euro zone crisis continues -- and widespread public resentment at the austerity measures shows no sign of diminishing – euro-skeptic parties such as the U.K. Independence Party (UKIP) and Alternative for Germany (AfD) have seen their share of the vote rise sharply, while support for more extreme right wing parties such as Golden Dawn in Greece or Norway's Progress Party has also risen.

The rise of euro-skeptic and far right parties signal trouble for the fractious 28-country EU and even more so for the 18-nation euro zone. The EU was founded to ensure economic prosperity – and thereby social development and cohesion -- across the whole of Europe. Its supporters argue that in a period of economic uncertainty, the EU's help is needed more than ever.

Supporters of the nationalist Serbian Radical Party (SRS) rip apart the EU flag.
Andrej Isakovic | AFP | Getty Images

However, euro-skeptics argue that the EU has become too bureaucratic; meddling in every aspect of a European's life. Furthermore, one of the EU's key tenets, the freedom of movement, is encouraging mass migration.

This rise in anti-European sentiment could come in May when elections are held for the European Parliament. If euro-skeptic parties such as UKIP win big, Europe's political bodies and economy could face the same kind of logjam that was seen in the U.S, analysts and politicians warn.

(Read more: UK election loss may force austerity rethink)

"If people in Europe today feel that there's no alternative to the far-right…then we're in trouble," David Martin, a Scottish MEP on the international trade committee, told CNBC.

"The far right could do very well in the elections…and it would also be very bad news for the European Parliament (EP) if they make the strong gains they are supposed to."

The European Parliament needs strong majorities to have influence the European Commission, the EU's executive arm, and when it comes to setting budgets and new laws, Martin said. But as euro-skeptic parties tended to abstain or vote "no" to any policies deemed even vaguely positive for Europe, the democratic process and function of the parliament itself could quickly come unstuck, he added.

"This would lead to further disillusionment with the parliament as an institution," Martin said, and could help anti-European, right wing parties grow further. More worryingly, although the rise of the right had been cause by the economic crisis, mainstream politicians had yet to provide the solution, Martin noted.

Yves Bertoncini and Valentin Kreilinger, director and research fellow respectively at the think tank Notre Europe-Jacques Delors Institute, forecast that the number of more "mainstream" euroskeptic parties will increase their national share of the vote in the elections.

In research published by the London School of Economics in December, they predicted that UKIP could receive 22 percent of the vote (up from 16.1 percent in 2009) and that the Front National in France would see its votes leap to 21 percent from 6.3 percent in 2009. (

They noted that the numerical increase of "populist forces" posed uncertainties for the European Parliament and warned that it "one thing is for sure: the political game is extremely open at this stage."

Euroskeptic parties have done well in European elections partly due to mainstream voter apathy, disillusionment and an increasing sense of detachment from the European "dream" of political and economic unity.

Will investors run scared of Europe's right wing?

In 2009, only 43 percent of all eligible voters in the then 27-nation EU turned out to vote – and in many of the individual countries the voter turnout was low, or high in countries, such as Belgium, where voting is compulsory.

Alastair Newton, senior political analyst at Nomura, told CNBC that investors who didn't think that EP elections were important were "wrong about that," adding that if a large number of nationalist parties were able to form a formal alliance, Europe could face "significant additional difficulties."

"Extensive wins for euroskeptic parties (i.e. around 30 percent of the seats according to some opinion polls) are likely to act as a drag on investor sentiment," he told CNBC.

Futhermore, Newton warned, "a strong showing by such parties will pull mainstream parties in government (and opposition, for that matter) into more euro-skeptic stances, "which is also likely to act as a drag on long-term stabilization – and, in many case I suspect, on pushing through structural reforms urgently needed to boost competitiveness and growth."

Unfortunately for European officials, the latter fundamentals are just what the region needs but as yet, there is no end to the euro zone crisis in sight. While euro zone unemployment is stuck at a record high of 12.1 percent, economic growth is near flat in both the EU and euro zone.

(Read more: Euro zone jobless at record high as retail sales surge)

As such, the vicious circle of little or no growth and increasing voter disillusionment could push more people into the arms of extremist parties. With names like "Freedom Party of Austria" or "For Fatherland and Freedom" in Latvia, far-right wing parties in Europe nail their colors firmly to the mast in terms of nationalist agenda.

Despite their controversial character, such parties have seen strong gains in national elections. For instance, Austria's Freedom Party gained 21.4 percent of the vote in national elections last year, not far behind the winning social democrats and conservative party.

"An economic recovery in the EU or debt relief in the euro zone would probably help [dispel the rise of these parties but] as neither are very likely, I expect we are in for a tough period for the EU," politics professor Rob Ford from the University of Manchester, told CNBC.

If such parties do as well as they are expected to in the elections, he added, the next European Parliament could prove to be "a very volatile and unpredictable institution."

"Governing Europe is already hard; it is about to get a lot harder," Ford added.

- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt.