Tony Blair could be an obstacle to winning a "yes" vote in the referendum on the European constitution, says a leading think tank.
Blair's credibility is a problem, says the report
Mr Blair must make way for Gordon Brown, Chris Patten and Charles Kennedy rather than wage a personal crusade, says the Foreign Policy Centre.
European leaders agreed a constitution in June but there will be a referendum.
Opinion polls suggest the "no" campaign is well ahead but the new report says 65% of voters are still undecided.
The report from the pro-European think tank aims to identify the "waverers" whose votes could be crucial in the referendum, which is not expected until after the next general election.
It includes a new survey conducted in July by opinion pollsters Mori, which suggests 31% of voters are currently in favour of Britain adopting the constitution and 50% against.
But 46% of those questioned said they might change their minds and another 19% said they did not know how they would vote.
In favour: 31%
Might change mind: 46%
Don't know: 19%
Source: Mori poll, July 2004
The report points to other recent surveys suggesting the public are dissatisfied with the prime minister by a two-to-one margin, with his credibility damaged by the Iraq war.
The Labour Party should resist any temptation to try to win a referendum by campaigning on Mr Blair's achievements, it says.
Otherwise, there is a risk voters could use the vote to give Mr Blair, who says he will lead the referendum campaign, a "bloody nose" between elections, it warns.
Foreign Policy Centre director Mark Leonard said: "Pro-Europeans cannot afford to let the constitution vote become a referendum on Blair.
"Two thirds of the public are ready to be swayed, but a campaign focusing on the PM will lose as many votes as it will gain.
"He needs to mobilise the whole government machine now - Brown, Prescott, Straw - and reach out to Charles Kennedy and Chris Patten."
The report argues that outgoing European commission Mr Patten, a former Tory chairman, should be the public face of the "yes" campaign and be put in charge of strategy.
Many of the "battleground" groups of constitution "waverers" identified in the report are those less likely to support Mr Blair, it says.
The report says more needs to be done to counter public ignorance about the EU.
Storylines should be suggested to television and radio soaps such as Eastenders or the Archers, it says.
In a foreword to the pamphlet, Labour peer and Britain in Europe board member Lord Radice says the "yes" campaign must begin now, despite the vote being probably months away.
"A conspiracy of silence by pro-Europeans... risks allowing opinion against the constitution to become set in stone making a yes victory even harder to attain," he says.
Former Labour Europe Minister Keith Vaz said Mr Blair was an asset, not a liability to the "yes" campaign.
Mr Vaz told BBC Radio 4's World At One: "You have to have the prime minister leading the campaign. It is such a central issue to the future of our country."
Critics of the constitution say it creates a European super state and gives more British powers to Brussels.
Meanwhile, a new centre-Left think tank is being set up to push for reform in Europe, including opposing the proposed constitution.
Labour MP Gwyneth Dunwoody, one of its backers, said critics of Europe were often dismissed as "little Englanders" and somebody needed to argue sensibly for change.
She said the debate should be on policies, not personalities.
"It is the day-to-day administration that is having an impact on our lives, not the pictures of Tony Blair," she said.