By Gavin Jones

ROME (Reuters) - Italian Prime Minister Matteo Renzi's hopes of winning his referendum on constitutional reform are dwindling fast as previously undecided voters are choosing to oppose his plan, according to pollsters.

Renzi has promised to resign if he loses the Dec. 4 ballot over his proposal to reduce the role of the Senate and transfer powers to central government from the regions, increasing political uncertainty in the euro zone's third largest economy.

The heads of several polling agencies contacted by Reuters said Donald Trump's surprise victory in the U.S. presidential election last week -- based on a wave of anti-establishment sentiment -- seemed to be a factor behind a widening lead for the 'No' camp.

Others had additional explanations, but all agreed that sentiment was hardening against Renzi, giving him a very tough task to turn around the polls in the next two weeks.

"There's a clear acceleration for 'No' and the Trump factor seems to have tipped the balance among many who were undecided," said Roberto Weber, head of the Ixe agency.

Of 42 polls by 15 different agencies since Oct. 21, every one has the 'No' camp ahead. And the margin is growing.

"Trump's victory was important because Renzi strongly backed Hillary Clinton and so people link him with the loser and the mainstream establishment that Clinton was seen as representing," said Alessandra Ghisleri, head of the Euromedia agency.

Ghisleri's latest poll gives 'No' a lead of eight percentage points, widening from four points just 10 days ago.

A welter of new polls were released on Friday, the last possible day because Italian law prohibits their publication in the 15 days before an election or referendum.

A survey by Ipsos PA for Corriere della Sera daily gave 'No' a 10 point lead. The Piepoli Institute for La Stampa put it at eight points, while another by Winpoll for the Huffington Post set it at seven points.

REBELLION

Pollsters said Trump's triumph appeared to have encouraged a feeling of rebellion against the established order which, in Italy, is represented by Renzi. But they also said that even without Trump the popular mood was moving against the premier.

"It's all about disenchantment with Renzi because the economic crisis isn't finished and the lives of most Italians aren't improving," said Renato Mannheimer, head of Eumetra-Monterosa, which gives 'No' a gaping 12 point lead.

"I don't think it has much to do with the constitutional reform itself," he added.

Just a few days ago, pollsters were still urging extreme caution about the referendum result, underlining how surveys came unstuck over Trump's victory and in the June 'Brexit' referendum in which Britons chose to leave the European Union.

However, now most say the size and consistency of the lead for 'No' is not comparable with the picture ahead of the U.S. election or Brexit, and it would take an unforeseen event in the next two weeks, or a remarkable surprise, for Renzi to win.

"Nearly all the undecided voters would have to vote 'Yes' for Renzi to recover, and that is certainly not the trend that we are seeing," said Mannheimer.

Polls vary over the number of voters still undecided, with estimates ranging from around 13 percent to 26 percent. About 40-45 percent are expected to abstain.

Factors previously cited as possibly helping Renzi, such as a low turnout in the poor south, where 'No' is very strong, or a big 'Yes' vote among Italians abroad, are still valid, pollsters say, but the lead for 'No' has become so large that they are unlikely to prove decisive.

"It seems those who back the reform were the first to decide and now we are seeing the undecideds, who are mostly less interested in politics, moving towards 'No' because they want to get rid of Renzi," said Federico Benini, the head of Winpoll.

"I think Renzi is going to lose."

(additional reporting by Massimiliano Di Giorgio Editing by Jeremy Gaunt)