Nearly three-quarters of people do not believe David Cameron will be able to deliver on his promise to bring 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 Mr Cameron's pledge of an in-out referendum by 2017 - come from a major piece of research commissioned by Tory peer Lord Ashcroft.