But if they vote No, it could be the beginning of the end of the eurozone.
The final opinion polls gave the No side a narrow lead, making this vote too close to call. "Second, the junior parties in the government coalition would have little interest in triggering early elections (nor would some of the opposition parties, particularly Silvio Berlusconi's Forza Italia)".
More specifically, she much disliked that the reform would change the rules for initiative bills: the minimum number of citizens' signatures to have them debated by the parliament would in fact increase from 50,000 to 150,000. Strengthened in this way, the argument goes, it could tackle urgently needed reforms. However, its focus on harnessing anti-euro sentiment and reshaping the political system are familiar.
Protesters in Italy have staged an anti-government demonstration in the capital city of Rome to protest against proposed constitutional reforms. "Such an outcome could throw into question the country's continued euro membership" - its use of the euro as money - "and could raise basic questions as to the eurozone's chances for survival in its present form".
Renzi announced he would resign if Italians voted No - but later backtracked. "It's a nervous market at a time when liquidity isn't great". He reiterated what he considers the importance of the vote for the future of democracy in Italy, but also noted the impact it will have if he is defeated by "no" voters.
Because a euro exit would take time and complex negotiations.
Renzi has proposed to punish them by curtailing European Union regional funding, which disproportionally benefits newer central and eastern European Union nations.
Most polls say the reforms will not be passed.
Manta Resort The underwater room at night- there are spotlights to attract shy creatures after dark
"The government has done its homework", said Jörg Buck, managing director of the German-Italian Chamber of Commerce in Milan. If Renzi follows through with his threat to resign if he loses the referendum, it may leave an opening for Grillo and other populist parties to force another vote on whether Italy should keep using the euro - thus the term "Quitaly" that defines the near certainty that Italy's rejection of the common currency would cause a continent-wide quake leading to the destruction of the EU.
The poor economic situation is weakening Renzi's position. Unemployment is over 12%, joblessness among young people runs at 40%. No to austerity. No to the establishment.
European stock markets fell on Monday as bank stocks hit the deck in a broad-based selloff.
They risked spiralling out of control during the sovereign debt crisis until ECB President Mario Draghi pledged in 2012 to do whatever it took to save the euro.
Why are financial markets anxious about Sunday's referendum?
Added to this is the unresolved crisis of Italian banks suffering under a mountain of bad loans. It comes with around 70 billion euros' worth of Italian bank bonds maturing in the coming year. "Either we change or I have no role to play", Renzi said this month - a line he regularly repeats at the frenzied round of rallies and media interviews he is undertaking before December 4. "UniCredit is set to follow suit later in the month". Renzi himself said that he expects high market volatility in the run-up to the referendum. Then there are the new populists, several PD old-timers, and plenty of other establishment figures, including several former members of the constitutional court, who generally fear change.
A "No" vote might trigger fresh elections in 2017 which will add to votes in Germany, France and the Netherlands which may have a profound influence on shaping the EU.