The ComRes poll, published last week, found that 71 per cent of party chairmen think that the proposals should be dropped and the same proportion said that Mr Cameron's attempts to legalise gay marriage had damaged his standing within the Party.
Six in 10 say legalising gay marriage will cost the Conservative Party votes.
The campaign group Coalition for Marriage, which is backed by many Christian leaders, said today that the poll reflected growing unease amongst Conservative grassroots supporters.
Campaign Director Colin Hart said: "The PM is trying to force through this policy without any electoral mandate and without any acknowledgement of the profound consequences this change will have."