Only 7% of Conservative supporters believe the party will win an overall majority at the next election, The Times has reported, with three quarters expecting Labour to be in power.
The newspaper cited the figures from a canvass of Tory supporters.
Conservative planning minister Nick Boles, though, has warned his party against swinging to the right following the drubbing in last week's Eastleigh by-election, which he said was the result of a "truly rotten campaign".
He said the party had failed to offer voters any hope in the Hampshire constituency and instead repeated the same mistakes it has been making "for a decade".
Mr Boles, an ally of the Prime Minister's, also warned any party schemers they needed "their head seeing to" if they believed it was wise to attempt to dethrone Mr Cameron.