ROME — Sunday's local elections in Italy are the last critical warmup match for Prime Minister Matteo Renzi before his biggest electoral test later this year.

The quarter of the country's electorate who vote this weekend will set the political tone going into October's referendum on proposed constitutional changes to shrink the power and size of the Italian Senate. Renzi has repeatedly stated that he'll quit if he loses that vote.

With the ruling Democratic Party (PD) almost certain to lose Rome's mayoral race, Renzi's center-left party needs to hold onto the business capital of Milan and other major cities to build momentum for the referendum campaign.

Some see only downsides for Renzi. "Renzi can only lose in these elections," said Francesco Galietti, CEO of Policy Sonar, a Rome-based political risk consultancy. "All five most important cities are strongholds of his party or the left at the moment, so it can only get worse."

Turnout among the 13 million eligible to vote is expected to be extremely low. The election falls in the middle of a long holiday weekend for many Italians. The last local election in 2015 saw unprecedented low turnout rates of around 50 percent in many locations. Polls suggest no candidate will win more than 50 percent on Sunday, which will trigger a second round of voting on June 19.

Virginia Raggi, the candidate of Beppe Grillo's anti-establishment 5Star Movement for mayor of Rome, had 32-35 percent support in the last polls done before a ban on polling went into effect on May 21, giving her a clear lead over the PD's Robert Giachetti and Giorgia Meloni of the far-right Brothers of Italy. Grillo is so confident of winning Rome that he promised to set himself on fire in public if Raggi fails.

"It is inevitable Renzi will lose Rome. Politically it's already lost," said Ilvo Diamanti, a political scientist.

If Raggi wins, the 37-year-old lawyer who was almost unknown until a few months ago would be the first woman to take power in the Campidoglio, ancient Rome's Capitoline hill, the mayoral palace designed by Michelangelo in the 16th century.

"Women [in Italy] cast their first ballot 70 years ago. I hope Romans want to change history by electing me as the first female mayor of Rome," Raggi said in an interview.

Penalty kick

Renzi's Democratic Party has not given up on Rome yet. Stefano Esposito, a PD senator, said that any candidate who makes it to the second round can turn the contest on its head.

"Let's not forget Rome's 2008 elections," he told POLITICO, recalling that in the two weeks between the first and second rounds the center-left incumbent Francesco Rutelli saw his six-point lead over Gianni Alemanno from the far-right Alleanza Nazionale evaporate.

In Milan, the prime minister's candidate Giuseppe Sala has a better chance of winning a second-round bout for the mayorship against the center-right's Stefano Parisi. The business capital is "the real battlefield" for Renzi, said Diamanti.

Campaigning for Sala earlier this week, Renzi piled on the pressure with a football simile, saying that winning Milan was like "a penalty that you have to strike well."

If the prime minister were to lose both Rome and Milan, his enemies inside and outside the PD could be galvanized ahead of the October referendum.

Besides those broader political considerations, Rome is a poisoned chalice, a city ridden with mismanagement, corruption and organized crime. Its finances are on the verge of collapse, with debts of over €12 billion. It averted bankruptcy last year after an emergency cash injection from the national treasury.

The last mayor of Rome, Ignazio Marino, resigned in October following an expenses scandal, which came on top of allegations that city hall had been infiltrated by the Mafia. Unelected bureaucrats have been running it since. "Rome has not been governed for the past 10 years, it's a political loss for whoever has to deal with it," Diamanti said.

No Catholic bloc vote

Raggi, a former city councilor for the 5Star Movement, blames the capital's problems on the incompetence of the mainstream parties, including the PD, saying they all "sold Rome to the banks."

"The Renzi government talks about flexibility in Europe but he's blackmailing the capital the same way the troika blackmailed Greece," she said, referring to the group of creditors who bailed out Greece.

With none of three main contestants constituting a suitably pristine choice for lay Catholics or the thousands of nuns and priests who fill the city's streets, the Vatican has failed to identify a mayoral favorite for the first time since 1946.

"The Pope is not interested in Italian politics, his electorate are the poor of the world. I think the times when Catholics voted as a bloc are over," said Marco Impagliazzo, head of the influential Sant'Egidio religious movement founded in Rome in 1968. He added, however, that the candidate closest to Christian social values is Giacchetti of the PD.

Renzi described the 55-year-old deputy speaker of parliament as "someone who knows Rome like few others." With the least charisma and most experience of the three contestants, Giachetti pulled ahead of Meloni late in the campaign and is likely to compete in the runoff.

Meloni's endorsement by the nationalist Northern League, which mortally offends Romans with its historic slogan Roma ladrona (Thieving Rome), may not have helped her in the capital. But the leader of Meloni's Brothers of Italy party, Fabio Rampelli, offered a different explanation: Speaking to POLITICO at a rally in the EUR neighborhood created by the fascist dictator Benito Mussolini, Rampelli blamed the pregnant Meloni's falling numbers on Silvio Berlusconi. The former prime minister had said that the role of mayor was not compatible with motherhood.