The outcome of Sunday's vote has thrown the country into renewed political turmoil, with the prospect of a sixth prime minister in a decade and frenzied talk that Italy could follow the UK and hold a referendum on its future in the European Union.
Italian President Sergio Mattarella is the man calling the plays on how the political situation will unfold. Renzi met Monday with Mattarella and offered his resignation, but he has been asked to remain until a budget bill has been approved on December 23.
The more likely scenario is that Mattarella will order the formation of a caretaker government led by a member of Renzi's Cabinet or a technocrat (someone with appropriate experience in government but not a politician).
The impact on Italy's financial markets will play a part, said Wolfango Piccoli, director of research at the global advisory firm Teneo Intelligence. Reaction so far has been fairly mild, but should the prospect of instability in the eurozone's third-largest economy move the markets significantly, he suggests Finance Minister Pier Carlo Padoan, a close ally of Matterella's whom investors largely respect, would be a front-runner.
"But the problem with him is that he will be seen as a continuity and that will spark further criticism from the (anti-establishment) Five Star Movement
, (former Prime Minister Silvio) Berlusconi and so on," Piccoli told CNN.
"If not Padoan, it could either be an institutional figure -- think about a former judge of the constitutional court, a safe pair of hands, or the speaker of the Senate, Pietro Grasso."
He added, "But at the end of the day, the name itself is not going to make a huge difference -- this is going to be a short-lived caretaker government with a very narrow mandate."
The next general election is scheduled for 2018, but it remains unclear if the interim government would wait and finish out the end of the parliamentary term or go to the polls earlier.
Following the "No" vote victory, opposition parties have called for a dissolution of Parliament and snap elections, but such moves would be unlikely.
Piccoli said "a coterie of anti-establishment parties" could gain from the win -- the most notable being the Five Star Movement and Northern League as well as another small extreme right-wing party, the Brothers of Italy.
Last year an electoral law, intended to build more stable governments, was passed that would give extra seats in Parliament to any party receiving votes of 40% or more. However, there is a constitutional court ruling pending on the law.
Mainstream establishment parties will want a rewrite on this bill before any early elections in an effort to prevent far-right populist parties from making significant gains in power.
"Electoral law will be used to somewhat defuse the risk of a Five Star Movement victory in the next election," Piccoli said.
"(These calls are) more about the claims that they won (Sunday) and that it is a major defeat for Renzi so the next step is an early election. But we know that (an) early election won't happen until the electoral system is changed, and this will take months, not weeks."
Is Italy more likely to leave the EU?
Whatever shorthand word the media settle on -- "Itexit," "Quitaly" or "Italexit" -- the stage is slowly being set for a battle over Italy's place in the EU. Far-right parties will want to capitalize on the momentum of the referendum victory and call for Italy's exit from the eurozone repeatedly in the coming months.
And while the loss of Renzi's reforms proposal hands Italy's EU skeptics a stronger mandate, it's not yet enough, Piccoli said.
"This was a vote against Renzi so it shouldn't be read as a vote against the euro, against the establishment," he said. "It is clear that the alarm bells have gone off in Italy now. ... There is going to be a certain sense of alarmism, but this is not a vote that will necessarily change the projection of Italy in the short term."
The result will certainly embolden the two important opposition movements -- the Five Star Movement and Northern League, said Chris Bickerton, a lecturer at Cambridge University and author of "The European Union: A Citizen's Guide." But actually tabling a vote on Italy's inclusion in the eurozone is still a long way off.
"It's pretty far-fetched as an immediate possibility," Bickerton told CNN. Instead, he said, Italians are now much more open to voting for parties that run on a more euroskeptic platform.
"It's a country that for so long has been one of the most enthusiastic countries for European integration. But I think over the last 10 years you'd have to say that that has changed."
He said suggestions the referendum could ultimately lead to Italy's exit from the EU are, at this point, "exaggerated."
"What (the result) does tell us ... is that a lot of people in Italy lost any sort of faith they put in Renzi as a reforming new figure in Italian politics," Bickerton said. "Since Italy joined the euro in 1999, it simply hasn't grown on average. It's had an average growth rate of zero so people do put two and two together and think this suggests that its place within the eurozone is not a very good idea."
He added: "Going from there to actually working out the mechanics of getting a referendum to leave the euro is something else. There is a climate in Italy of growing euroskepticism and certainly anti-establishment feeling -- that's very clear. The implications for the EU specifically, I think, are probably less clear."