Previous administrations have tried to make a dent in Italy's public debt, which is predicted to finish this year at 132.8 percent of output, close to the 132.9 percent at the end of 2013 - the highest level of euro zone countries apart from Greece.
Renzi faces a "steep and bumpy climb" as he tries to push through an ambitious timetable of reforms to the country's economy, education and judicial system, Credit Suisse analysts pointed out in a research note.
"The necessary reforms for the country are well known and documented," they wrote. "However, opposition inside and outside the parliament and inside and outside the public administration has curtailed most of their efforts. And Renzi is likely to face similar challenges."
(Read more:Italian 'Demolition Man' takes charge)
It comes as international bond investors desert the country - net demand for Italian bonds fell to at a six-month low over the four weeks to February 24. This follows proposals to raise the bond coupon tax to 20 percent from 12.5 percent.
Italy's benchmark stock index, the FTSE MIB, has risen slightly since Renzi's appointment, but analysts cautioned this may not be a vote of confidence in the new Prime Minister so much as a continuation of reignited investor interest in European equities.
"(The new government) is business as usual, which is slow progress," Michael Gallagher, director of research at IDEAGlobal, told CNBC.
- By CNBC's Catherine Boyle. Twitter: @cboylecnbc.