“Now it’s our turn,” the leader of Italy’s ascendant far right, Matteo Salvini, said at the time about exiting the European Union.

But the 2016 Brexit vote has spawned no copycats. Nor did it lead to the crackup of the E.U. Even the most ardent Brussels-bashing politicians have concluded it is better to stick with the bloc than endure a messy, years-long divorce.

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On Friday, the day Britain was supposed to leave the E.U. and “take back control,” the British Parliament was still fighting over how and whether to leave. Lawmakers rejected, for the third time, the withdrawal deal negotiated between Prime Minister Theresa May and E.U. leaders. The pound fell on fears that Britain will abruptly crash out of the bloc on April 12, with massive disruptions to trade and travel.

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Even if Britain manages an orderly departure, economic forecasters say Brexit could dampen growth for years. And the political and social divisions between “leavers” and “remainers” may persist.

Watching all this, the continent’s influential Euroskeptic parties — from Scandinavia to the Mediterranean — have recast their message. They have dropped calls to leave the E.U. and are instead advocating for the less drastic approach of changing the bloc from within. The European political scene has scarcely a party remaining advocating for a Brexit-style departure.

“There has been a shift, definitely a shift,” Stephen K. Bannon, a former White House chief strategist who consults with nationalist parties in Europe, said in an interview. “The agony of Britain in the last two years has clearly been a subtext for ‘Let’s try to make this thing work’ ” within Europe.

The shift does not mean that the E.U. has averted turmoil or that Europe’s political insurgents are happy with the status quo. Europe’s class of populists and nationalists — a mix of ruling parties and clamorous outside voices on the left and right — remains buoyed by discontent over low economic growth, migration and the perceived imperiousness of E.U. elites. Those populists want to decentralize power within the E.U. and are hoping to use European parliamentary elections in May to expand their influence and carry out their ideas.

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But even as Europeans find reason to grumble about the bloc, voters do not seem to have the appetite for an irrevocable split. In fact, some have grown fonder of the European Union.

The E.U.’s approval rating increased sharply in 2017 as Britain began to debate the terms of its exit. A new Pew Research Center survey of 10 European nations shows that 62 percent of people hold a favorable view of the E.U.

A separate poll from last year showed that 67 percent of Europeans believed their country benefited from E.U. membership — the highest figure in 35 years.

“You had the Brexit referendum. Also the Trump election,” said Stefan Lehne, a visiting scholar at Carnegie Europe in Brussels. “It created a lot of fear and uncertainty, and the response [from Europeans] was, we want the known over the unknown.”

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From Hungary to Sweden, Germany to Italy, Euroskeptic politicians are now trying to figure out just how much of a mandate they might have to upend Europe’s norms. It is not as clear a calculus as it had been.

The reasons to stick with Europe go beyond a distaste for Brexit redux. A significant number of Europeans, even those who support Euroskeptic parties, appreciate the freedom of movement allowed by E.U. rules and the ability to live in other countries. They also like the outsize influence of the unified bloc, which makes it easier for countries to contend with China and the United States.

For now, some parties have simply dropped exit-the-E.U. plans from their platforms. Others have made concessions or adapted after political setbacks. In Austria, the Freedom Party abandoned calls for a euro referendum before joining another party in a coalition government. In France, nationalist leader Marine Le Pen called in her 2017 campaign for a referendum on euro-zone membership and badly lost an election to Emmanuel Macron. Now she speaks instead of a “Europe of nations” that works better for its members.

And in the Netherlands, when the face of the anti-immigration far right — Geert Wilders — said in a televised debate that a Nexit would be the best thing that could happen to the country, the incumbent prime minister accused him of scaremongering.

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“You want to push the Netherlands into chaos, too,” like in Britain, Prime Minister Mark Rutte said.

Wilders’s party fared worse than expected in Dutch elections.

But it is in Italy where the evolution of the populist message on Europe is perhaps most stark. The country’s government is composed of two Euroskeptic parties that cheered Britain’s Brexit vote when it happened. Now, those parties say it would be inconceivable to follow suit.

“It’s not feasible,” said Claudio Borghi, a parliamentarian from the League. “There wouldn’t even be a majority to get to that.”

Salvini’s far-right League and the more politically amorphous Five Star Movement used to be more vocally hostile to the E.U. They accused fellow member states of abandoning Italy in its efforts to deal with migration while saddling it with unhelpful economic rules. Salvini held rallies wearing T-shirts that read “Enough with the Euro.” The Five Star Movement, too, had long called for a referendum on Italy’s euro membership. For a time, it maintained a parliamentary alliance with the U.K. Independence Party, whose onetime leader Nigel Farage was a driving force behind the Brexit campaign.

But Italian politicians say both parties have changed tactics — in part as a result of having to govern but also because of a changing mood.

Last year, neither party campaigned heavily on the idea of leaving Europe, and when the coalition proposed an economy minister who had called the euro a “historic error,” the country’s referee-like president stepped in and told it to find somebody else. President Sergio Mattarella said any discussion on leaving the euro would first need a serious and public “in-depth analysis.”

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Salvini no longer uses the hashtag #BastaEuro. Major Five Star members no longer retweet calls for euro referendums. Borghi — a League hard-liner who remains vocally opposed to the E.U. — recently said Italy should consider leaving the bloc if things do not change radically; Salvini later that day said he had no plans to leave or “abandon” Europe.

As messy as Brexit has been, the exit process could be even more turbulent for a euro-zone nation that would have to contend with not only customs and border headaches but also the introduction of a new currency — or the return to an old one.

Marta Grande, a Five Star member who heads a parliamentary committee on foreign affairs, said that within her party, views on Europe were all over the map several years ago. But those views have gradually converged on the idea that the European Union needs to be criticized constructively and improved. She acknowledged that politicians in Italy continued to cast blame at Brussels but said, “People don’t want to leave the E.U.”

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An Italian research group, the Carlo Cattaneo Institute, tracked Five Star Movement votes in the European Parliament and found they in some ways resembled the voting patterns of a traditional Green party — left-leaning and somewhat pro-European.

“If I see how we behaved five years ago, we were so naive regarding so many issues,” Grande said. She said the idea of a referendum on the euro “was something to say during the electoral campaign rather than a real attempt to do it.”

Both Salvini and Luigi Di Maio, the head of the Five Star Movement, have launched campaigns for the May parliamentary elections; both have called for E.U. overhauls. Salvini has minted a new slogan: “And now we change Europe.”

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Analysts say that insurgent parties across Europe hope to curtail E.U. power over budget-making and bring their hard-line migration ideas to Brussels.

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But the elections are a referendum on the strength of the union — not on whether the union should exist.