Asking senators to vote for their own abolition was always going to be a tough mission – even for the ever-confident Matteo Renzi. So it is hardly surprising that the Italian prime minister's flagship reform bill – on which he has staked his career – has run into a few problems in the upper house of parliament – 7,850 of them, to be precise.

Opponents to the proposals – which would see the senate stripped of many of its powers and become a much smaller, unelected regional chamber – have tabled nearly 8,000 amendments which they want debated before the upper house moves to a first reading vote.

On Wednesday, when the debate began in the senate, just three were dealt with. "Another 7,847 and we're there," quipped the Corriere della Sera newspaper. "Congratulations."

In the face of what one commentator called an "abnormal mountain" of opposition, the 39-year-old prime minister seems, in public at least, undeterred, insisting with trademark certainty that a vote will be held before the summer recess in mid-August.

But Italy's 89-year-old president, Giorgio Napolitano, is rather less relaxed.

On Wednesday night, during a meeting with the president of the senate, Pietro Grasso, he was reported to have "insisted on the serious damage that a paralysis in decision-making on an essential process of reform would do to the prestige and credibility of parliament".

Earlier this year Renzi, who came to power in a party coup in February, said he would "accept the consequences" if his flagship constitutional reform was blocked by parliament. He argues the changes are essential if Italy is to adopt a more stable and streamlined political system.

But there are fierce challenges from senators in the opposition Left Ecology Freedom (SEL) party and Five Star Movement (M5S) – as well as some within Renzi's own centre-left Democratic party, coalition partners and Silvio Berlusconi's centre-right Forza Italia.

In a cross-party pact deemed almost Faustian by critics on the left, Renzi has a deal with the former prime minister, whose party is in opposition, to push through the senate reform – and others. After he was acquitted in a high-profile underage prostitution trial last week, Berlusconi indicated that his party would honour its agreement.

But he remains an uncertain reform partner and, moreover, the perils to Renzi's timeframe are clear. As well as the huge dossier of amendments, there have been more than 900 requests for voting to be carried out via secret ballot.

On Thursday the minister for constitutional reform, Maria Elena Boschi, dismissed the possibility of examining all 7,850 amendments. "The government is still willing to improve the draft, but not to change it completely," she was quoted as saying.

Maurizio Sacconi, senate head of the government's coalition partner the New Centre Right party, demanded the number of amendments be "drastically reduced" or a system of time limits be imposed to make sure a vote was held on time.

Opponents accused the government of giving an ultimatum. "They are trampling on democracy," said one M5S senator, Bruno Marton. "They just want to steamroller through a reform that makes no sense."

The SEL leader Nichi Vendola reportedly said he hoped the threat of time limits was a "joke … because this really stinks unbearably".