By Isla Binnie

ROME (Reuters) - Matteo Renzi gazes out from the cover of this month's Italian edition of Rolling Stone magazine as if performing a blessing.

He is "The Young Pop", the magazine says in a riff on the title of a new television series about a fictional pope and on Renzi as popstar.

Renzi, 41, who became Italy's youngest ever prime minister two and a half years ago, needs to lure young voters who might read Rolling Stone if he is to win a make-or-break constitutional referendum on Dec. 4. So far, he is struggling.

With just over a month to go until the referendum which will define Renzi's political career he is lagging in the polls, which also show a stark generational split.

A survey by pollster IPR on Oct. 17 found that 60.5 percent of 18-34 year olds planned to vote against the proposed constitutional reform to reduce the role of the upper house Senate and curb the powers of regional governments.

That compared with 39.5 percent who plan to vote in favor. The proportion was exactly the opposite among over-55s.

The lack of youth support may stem from cynicism about what Renzi has promised and what he has achieved. For many, Renzi's previous initiatives have yet to make tangible progress in reversing Italy's grinding economic decline, which has hurt the young more than the old.

A pledge to reform and break down old structures blamed for economic weakness and political instability once earned him the nickname "Demolition Man", but many now feel he promised a bigger break from the past than he could deliver.

"If you promise great reforms and then make huge compromises you're not a 'Demolition Man," said Alessandro Aceto, a 26 year-old engineer from Monza.

YOUTH UNEMPLOYMENT, POVERTY

A report last week by Milan's Bocconi University and U.S. bank J.P. Morgan showed 15-24 year-olds make up 20 percent of Italy's long-term unemployed - those who have been unable to find work for more than a year.

The gap between youth unemployment and adult unemployment rose steeply between 2007 and 2015, the report said. The overall youth unemployment rate has remained stubbornly close to 40 percent during Renzi's entire mandate.

"These voters feel disadvantaged, they haven't seen improvements, and they probably had great expectations of Renzi," said Antonio Noto, head of pollster IPR.

A new labor law which made it easier for private companies to fire workers only applies to new hires, while changes to the pensionable age by a previous government mean their older colleagues stay in the workforce longer.

Absolute poverty in Italy is at its highest rate for a decade and Catholic charity Caritas said in October 47 percent of people who fall into that category are under 34 years old.

The referendum question has been criticized for cramming too many issues onto one voting slip, and fewer than 20 percent of those polled by IPR said they understood it well.

Against the backdrop of complex constitutional change, 30 year-old marketing executive Flavia Carcano said the Rolling Stone appearance was a good idea.

"He's trying to be closer to young people and speak the same language as people who have been uninterested until now."

The polls would suggest a hard climb.

(Reporting by Isla Binnie, editing by Gavin Jones)