Not even 1 in 3 Lib Dem voters still back the party: Despite by-election victory, Clegg faces a hammering in 2015 Survey says just 29 per cent of 2010 Lib Dem voters would do so again Other 71 per cent say they would vote for another party, or don't know But a quarter of those who would vote Lib Dem, did not do so in 2010 Fewer than a third of Liberal Democrat voters at the last election plan to back the party again, a major poll reveals today. A survey commissioned by former Tory deputy chairman Lord Ashcroft suggests there is little room for complacency for Nick Clegg despite the by-election victory in Eastleigh last week. As the Lib Dems prepare for their spring conference in Brighton, starting tonight, the research suggests Mr Clegg faces a dilemma as he attempts to rebuild support. Research: There is little room for complacency for Nick Clegg despite the by-election victory in Eastleigh last week, according to a survey commissioned by former Tory deputy chairman Lord Ashcroft (right) While many left-leaning former Lib Dem voters want the party to be more vocal in opposing the Tories, such a move would put off more moderate, Conservative-leaning voters who might otherwise stay with the party or even switch to it. Lord Ashcroft's research, based on a poll of more than 20,000 voters, finds that only 29 per cent of those who voted Lib Dem in 2010 say they would do so again tomorrow - just 5 per cent of the electorate. The other 71 per cent say they would vote for another party, or don't know. However, nearly a quarter of those who say they would vote Lib Dem in an election tomorrow did not vote for the party in 2010 - indicating the party has picked up significant support since entering government. Some 29 per cent of Lib Dem voters in 2010 now say they would vote Labour or Green - with many angry that the party joined the Coalition. Another 8 per cent of 2010 Lib Dem voters would now vote Conservative, with 7 per cent backing UKIP. More than a fifth - 22 per cent - of those who voted Lib Dem in 2010 do not know how they would vote tomorrow. Though many have lost confidence in the Lib Dems, they are resistant to Labour and do not know who to trust on the economy. The Lib Dems" flagship economic policy - raising the income tax threshold to £10,000 - is backed by an overwhelming 85 per cent of voters, but four in ten think it was a Tory proposal. The most recognisable Lib Dem policy is an amnesty for illegal migrants, which only 25 per cent of voters support and has not been implemented in government. Lord Ashcroft, who is now a leading pollster, said: "After the Eastleigh by-election Lib Dem activists will be relieved to think that despite the polls, strong local government and an invincible leaflet-dropping network will see most of their MPs safely back to Westminster. But that is not the whole story. Localness matters, but a general election decides who walks up Downing Street. Clegg must have something to say about the Liberal Democrats and government. Lord Ashcroft warned the Tories would learn the "wrong lessons" from the Eastleigh by-election if they chased the UKIP vote as this would leave moderate and centre-right voters "wide open to the Lib Dems." In a pre-conference interview, Lib Dem president Tim Farron spoke frankly about the Eastleigh result. He said: "We're a bit like cockroaches after a nuclear war, just a bit less smelly. We are made of sterner stuff. The party is in a critical state. We may well be cockroach-ish, but we shouldn't take that for granted. One day someone will stand on us if we are not careful. We shouldn't assume our survival is guaranteed. Nick Clegg yesterday angered Mid Staffordshire victims by saying NHS chief Sir David Nicholson should stay in his job because sacrificing him might "let the system off the hook." Health Secretary Jeremy Hunt will today say hospitals are killing patients by "coasting along" with "low expectations." Poll: Nick Clegg and wife Miriam Clegg outside the polling station to cast their vote in their constituency home in Sheffield in the 2010 general election