Nearly three-quarters of people do not believe David Cameron will be able to deliver on his promise to claw back powers from the EU, according to a poll.
Some 51% think other members will block reforms, while 26% doubt the prime minister's skills as a negotiator. Almost one in four suspects he wants to stay in the union even if Britain does not achieve a better deal.
The findings - which cast doubt on the electoral effectiveness of Cameron's pledge of an in-out referendum by 2017 - come from a major piece of research commissioned by Tory peer Lord Ashcroft.
Of the 20,000 people questioned, around two-thirds said other countries benefited more from the EU than the UK.
Some 49% thought the drawbacks of being a member outweighed the advantages - compared to 31% who said the opposite and 20% who were not sure either way.
Just one in 10 could name an MEP in their area.
The survey also suggested people had a more positive view of Russia than of the EU.
The European Parliament came fourth from bottom in a league table of 27 "liked" countries and institutions.
Only Saudi Arabia, Iran and North Korea were placed below it.
Lord Ashcroft told the Sun on Sunday: "Many like David Cameron's plan to negotiate better terms for Britain.
"The trouble is, three-quarters of them doubt it will work. Most of the pessimists think other countries will not be prepared to make concessions to Britain however well the PM argues the case.
"Others question his ability to persuade or think he wants Britain to stay in the EU regardless.
"But those who say the whole country is clamouring for a referendum are wrong. Some, certainly, think it is the greatest question of our time. But even among the most hostile voters, only a third put Europe among the most crucial issues facing the country.
"That is why Cameron's 'negotiate and decide' policy will please some voters but won't win the election all by itself."
The peer cautioned that many people felt they did not "know enough to make such a fundamental choice about Britain's future".
He wrote: "My polling shows people will want to be reassured about our prospects outside the EU before making the leap - and that the better-off-outers in particular need to take care not to sound too batty.
"The pro side, meanwhile, seem hesitant about their case. Fear of the unknown is their greatest ally, but many voters want to hear more than a defensive message that Britain can't survive alone."
A Number 10 source said: "The PM has already proved he can get a better deal for Britain in Europe. He vetoed a damaging EU treaty, pulled the UK out of a costly EU bank bailout and cut the Brussels budget for the first time in history.
"He can and will deliver a better deal for Britain in Europe - and the Conservatives are the only party that can deliver a referendum and give the British people the final say on whether to stay in a reformed EU or leave."