The proposed reforms - deemed the most important in Italy since World War II - would streamline parliament and the electoral system in the hope of bringing the country badly-needed political stability.
But the vote is shaping up as a referendum on Renzi's two-and-a-half years in office.
The reforms, approved by the two chambers of parliament earlier this year, would bring an end to the existing system whereby each law must be adopted by both chambers in the same terms - a process that can take years.
The system was put in place after World War II in a bid to avoid any return to fascism.
Today, though, it is widely seen as a source of political paralysis and instability, leading to 63 governments since 1945.
Since 2010 alone Italy has had four prime ministers: Silvio Berlusconi, Mario Monti, Enrico Letta, and Renzi himself, who has had to fight opposition pressure to stand down over a sleaze scandal.
'Personalizing the vote was a mistake'
The reforms would greatly reduce the role of the Senate, and the numbers sitting in it from 315 to 100.
The upper house would not take part in confidence votes in the government and would deal with a limited number of new laws.
Renzi initially promised he would quit if the measures are voted down at a referendum.
Since then, he has repeatedly nuanced those words, saying he had "committed a mistake by personalizing" the vote but had merely sought to convey "a message of seriousness and responsibility."
He has vowed to campaign intensively, taking his message "from house to house" if necessary. Renzi's critics have set up an organization called the Committee for No, hoping that he will be swept away, or at least weakened, if he loses.
His opponents include rightwing and leftwing opposition parties and the populist Five Stars Movement, as well as members of his Democratic Party, Italy's main centre-left political group.
The latest opinion poll gives a slight edge, of 51 to 49 percent, to the "Yes" vote.