A "no" vote in Sunday's referendum would not quite be Italy's Brexit moment, because in theory it would simply reject a package of constitutional changes designed to shake up a chaotic political system that has had 63 governments in the past 70 years. But the moment has turned into an up-down vote on Renzi's 2 1/2-year-old premiership, as opponents seek to seize on his political weakness.
A Renzi rejection would be a boost for Italy's burgeoning Five Star Movement, which has capitalised on voter discontent to sweep into mayor's offices in Turin and Rome and vowed to conduct a referendum on Italy's membership in the euro currency the moment it captures the prime minister's office.
The outcome has pressed on President Obama, who used his final state dinner to host Renzi in Washington in October, trying to boost his embattled Italian counterpart.
"I won't weigh in on the referendum, but the reforms Matteo is initiating, certainly on the economic side, are the right ones," Obama said. "And in a global, Internet-driven world, governments have to be able to move fast and quickly and transparently."
Renzi's populist opponents have embraced Trump, meanwhile, and Trump met briefly with Matteo Salvini, the head of the anti-immigrant Northern League party, in the spring.
For now, the outcome of the referendum is too close to call. Polls published before a two-week blackout period gave "no" a slight lead, but Renzi and his allies are gambling that a last-minute campaign push will tip them over the finish line.
What is certain, however, is that the race has deeply split the country.
Even some of Renzi's allies in his centre-left Democratic Party have abandoned him, as have other establishment grandees, including several past prime ministers. They say the laws are poorly written and would create as many problems as they try to fix.
"I do not believe this reform will achieve the main objective for which it was set up, which was to streamline the governance of Italy," said Mario Monti, the economist who took over from Silvio Berlusconi as Italy's technocratic prime minister in 2011. He criticized Renzi for taking a page from the anti-establishment playbook by slamming the E.U. for its policies on the economy and migration.
Renzi, nicknamed the "scrapper" for his combative political style, took power promising to shake up Italy's stagnating political system. Now 41, he was the youngest Italian premier in history, fond of Twitter, Apple gadgets and Coca-Cola. And he enjoyed initial success in pushing through a number of economic reforms that made it easier for employers to hire and fire employees, a measure that made him unpopular with labour unions but was an attempt to jump-start Italy's flatlined economy.
The constitutional reforms would overhaul Italy's overstuffed upper house of Parliament and, advocates say, improve lawmaking.
"A 'yes' to this reform is a yes to change. The best ally of populist movements in Italy is the status quo," said Sandro Gozi, a top Renzi ally who is the undersecretary for European affairs in the prime minister's office.
"Vote thinking of your children, not of me or of the government," Renzi said this week, seeking to shift attention away from his political future and back toward the text of the changes.
In an ominous sign for the long-term prospects of centrist Italian parties, local opinion polling showed that support for the constitutional changes is strongest among voters over 65 and weakest among Italian youth, who have gravitated toward the Five Star Movement and other anti-establishment parties amid sinking optimism about their future.
The Five Star Movement has vowed to hold a referendum on membership in the euro currency zone if ever they capture Italy's top office, a step that could ultimately split the entire E.U. The fiery leader of the party, comedian Beppe Grillo, has praised Trump's attitudes toward immigrants and vowed to build an Italian version of his triumph.
Supporters of the Five Star Movement and of other anti-establishment rebels in Italy say that Renzi's attempt to revise the constitution was simply a power grab that would do little to address the problems closer to voters' hearts: stubbornly high unemployment, rampant corruption and record numbers of migrants from Africa arriving on Italy's shores.
"In Italy there are two emergencies," said Salvini, the leader of the anti-E.U. Northern League party. "Employment and security."
"We're trying to form alliances in order to change Europe," he said.
They are finding a receptive audience.
"Italian democracy is a sham," said Pasquale La Marca, 24, a black-leather-clad clothing-stitcher from Naples who said that he planned to sit out Sunday's referendum entirely. He complained that no one in power listened to ordinary people.
Analysts caution that there are some roadblocks to the Five Star Movement's progress. Its leadership of Rome has been chaotic and unpopular, suggesting leaders may have difficulty transforming into a governing party. And if Renzi loses the referendum, Italy's mainstream parties are likely to revamp an electoral law that would dilute the ability of populist parties to seize power.
Separate from any populist surge, a loss for Renzi may simply be an indicator of his own political missteps.
"The Five Star Movement is just a reflection of the fever of the system. If the system is working well, the fever will go down," said Massimo Franco, a political columnist for Corriere della Sera.
Even if Renzi pulls off a victory, the populists may have made their mark. Allies say he may use any success to focus closely on the populists' pet issues.
"We don't have to be populist, but we have to be close to the people," said Infrastructure and Transport Minister Graziano Delrio, a top Renzi surrogate. "A lot of people do not feel like protagonists in society, but outsiders."
