Conservatives suffered fresh opinion poll woe as the UK Independence Party (Ukip) continued to register record highs.
In results that will fuel MP and grass-root fears the party is haemorrhaging support over Europe, the economy and gay marriage, Tory backing slumped in two surveys.
Populus for The Times showed a drop of six points to 29%, its lowest rating with voters during David Cameron's seven-year leadership.
It put Ukip up six at 10% - its highest in that poll - with Labour unchanged on 40% and the Liberal Democrats up two at 11%.
Another carried out for The Independent by ComRes had a four-point dip for the Tories to 31%, with Ukip up three on 9%, Labour down one at 41% and the Lib Dems unchanged with 10%.
The Prime Minister told MPs that a British exit from the EU was an "imaginable" option in what will be seen as a hint the option could be offered in a referendum.
Asked if he could imagine the prospect of withdrawal he insisted he supported continued membership but added: "Clearly, all futures for Britain are imaginable.
"We are in charge of own destiny, we can make our own choices," he said ahead of a long-delayed speech next month in which he will set out plans for a referendum on relations with Brussels. The Times poll suggested voters were increasingly hostile towards the EU, with more than three now believing Britain would be "better off out" - up three points.
At the weekend, Ukip recorded 14% support in two poll, overtaking the Lib Dems which leader Nigel Farage said it was now supplanting as the third party in Britain.
He is also targeting Tory supporters upset at Mr Cameron's decision to push through proposals for same-sex marriage and claims it could lose one in five supporters over the issue.
Although Tory MPs have been promised a free vote on the issue, there is deep anger among traditionalists in the party who say it is out of step with the instincts of their natural supporters and is driving away the activists they need to campaign for them.
Some 35 put their names to an open letter to the Daily Telegraph yesterday warning ministers they have no mandate for the proposed change.
Populus interviewed 1,512 adults by telephone between December 14 and 16. ComRes interviewed 1,000 GB adults by telephone between December 14 and 16.