The tweet from Italy’s most rightwing xenophobe was enough to send a chill down any liberal democrat’s spine.

In the face of a resounding defeat of centre-left prime minister Matteo Renzi, Northern League leader Matteo Salvini wrote: “Viva Trump, viva Putin, viva la Le Pen e viva la Lega!” It was swiftly followed by a note of congratulations from Marine Le Pen, who said the Italian electorate had “disowned the EU and Renzi”.

It was clear from the high voter turnout – 68% of eligible voters cast ballots on Sunday – that Italians were indeed sending a message to the political establishment in Rome. But deciphering that message will not be easy, despite celebratory claims from Europe’s far right.

Italy is facing a number of big issues that were not technically on the ballot: a migration crisis in which the country feels abandoned by Europe; an unresolved banking crisis; steep unemployment and a debt load of 132% of GDP with no solution in sight.

The fact is that Renzi’s defeat was almost a foregone conclusion give the scale of the opposition he faced, and not just from Salvini and Beppe Grillo, the bombastic former comedian and head of the Five Star Movement. But even from within the Democratic party and leftwing voters who defied the prime minister for a whole host of reasons, including a former prime minister, Mario Monti.

On his blog, Grillo called the referendum results a victory for democracy. “The propaganda of the regime and all of its lies are the first losers of this referendum,” he said. It was a pointed remark following several reports, including in La Stampa, Buzzfeed and the New York Times, that alleged the Five Star Movement was behind an intense disinformation campaign and that officials in the Renzi government had raised concerns about possible Russian influence in Italian politics.

The Five Star Movement has denied it was linked to propaganda or so-called “fake news”.

Like the Northern League, however, Grillo has said he would demand snap elections, suggesting both believe the large margin of victory in the no camp would translate into big wins in a national election.

But that is not necessarily clear. The constitutional reforms that were proposed by Renzi were passed by parliament in early 2015 when he was far more popular, but did not pass with enough support to allow him to bypass a referendum. The reforms would have made drastic changes to the country’s constitution, which was crafted in 1948 in the wake of the second world war by Italians who did not want to see the country fall into fascist hands again.

While Salvini and M5S officials have touted the win as a major victory for their causes – they are not totally aligned but are vehemently opposed to the euro and the EU generally – it is clear that many Italians who voted no would not necessarily support either party in a general election. Indeed, some were indifferent to Renzi’s fate but believed the rise of populism made proposed changes to the constitution especially dangerous.

The undeniable boost to the Five Star Movement and the Northern League could solidify a historic allegiance between Italy’s two traditional parties – Renzi’s Democratic party and Silvio Berlusconi’s Forza Italia – in order to block more possible gains for the anti-establishment groups.