Were the Conservative party a ship, it would now be holed dangerously near the water line. This is clear from YouGov polls for the Sun and Sunday Times ahead of this week's party conference. Since Ed Miliband's speech last Tuesday to Labour's annual conference, the Tories have slipped back to 31-32% - the same share as in their crushing defeats in 1997 and 2001. On any question that compares Miliband with David Cameron, Labour's leader has made significant advances.

Even more worrying for the Tories should be the questions that do not involve any comparisons with the opposition. These show that Cameron and the Conservatives have not just slipped against Miliband and Labour. They are unpopular in themselves:

- Fewer than 30% think they have done a good job on health, education, transport or reforming welfare benefits.
- Most people think they have made no progress at all to get Britain out of recession, reduce immigration, clean up politics, or fulfil their pledge to make theirs "the greenest government ever".
- 71% think the gap between the richest and poorest has widened since the Tories came to power; and by two-to-one, people think the north-south gap has also widened. (Northerners themselves agree by three-to-one.)
- Just 13% say the government has met their expectations that Britain would be governed well; far more, 34%, say "I expected them to do well, but they have been a disappointment". Half of those who voted Conservative in 2010 share this sense of disappointment.
- Only 10% are now "very clear" what Cameron himself stands for. When we ask whether he has become clearer or less clear about this since he became Prime Minister, just 8% say he has become clearer, while 43% say less clear.

The Conservatives' problems are compounded by the unpopularity of their coalition partners, the Liberal Democrats. Most of the anti-Conservatives who voted Lib Dem in 2010 have returned to Labour. This is by far the biggest single reason why Labour's support remains above 40%.

Now, I expect the Lib Dems to recover some support at the next election. However, the chances are that many of these defectors won't return. Unless Miliband screws up completely (and after his performance last week, that likelihood has receded) Labour looks unlikely to slip below 35% at the next election. If so, then the Tories will need at least 42% to win a clear majority. This requires a five-point increase on last time: a surge that no governing party has achieved since Lord Palmerston led the Liberals to victory in 1857.

Records, of course, are made to be broken. Were Cameron to break this one, his achievement would be historic. Actually, I'm not sure 'historic' is quite enough. Given the fragility of Britain's economy, the prospect of further cuts to our public services, and the UK Independence Party wooing Tory voters on the euro-phobic Right, 'miraculous' might be more appropriate.

Can it be done? If the Conservatives are to stand any chance, they must do three large things. First, they need to regain their reputation for competence. The party has often won elections despite being widely seen as divisive and out of touch. Forced to choose, millions prefer hard-hearted bastards who know how to run things, rather than soft-hearted angels who couldn't run a fruit stall (do whelk stalls exist anymore?). The Tories' big problem these days is that many see them as incompetent bastards: not just heartless, but hopeless.

That is why so much damage is done by stories such as the screw-up over the West Coast rail franchise. Forget the details - how blame should be allocated between officials and ministers - what matters is that this has happened on the Tories' watch. As far as voters are concerned, it fits a pattern of dither and ineptitude. Think of this year's Budget, the controversies over NHS reforms, the lack of a clear decision on Heathrow's third runway and - above all - the failure to boost economic growth and reduce the government deficit. In short, the ministers have been guilty of the sin that has been fatal to so many businesses. They have over-promised and under-delivered.

In order to stand any chance of recovery, the Conservatives need to lower public expectations. For the next two years they must under-promise and over-deliver. At a time of austerity, under-promising is bound to sound bleak. However, better bleakness now, than a verdict of failure in 2015.

The second large task for the Tories is to support their leader in a more united and emphatic way than they are doing just now. For all the public disappointment in him, David Cameron remains their greatest asset. He still leads Miliband when people are asked who would make the best Prime Minister, albeit by a narrower margin following Labour's conference last week.

There may come a time when Cameron is a liability and needs replacing. Historically, the Tories have been good at regicide, as Edward Heath, Margaret Thatcher and Iain Duncan Smith discovered. But for regicide to impress the public enough and win back lost votes, it should be sudden and decisive. A slow battle of attrition is the worst possible way to remove a leader.

Thirdly, Cameron needs to improve his personal reputation. He may still be his party's greatest asset, but he is less popular than he used to be. However, pretending to be a normal bloke won't do the trick. One thing he should NOT fret over is being an old Etonian. He can't change his past; besides, there's no evidence that voters prefer their politicians to be paupers instead of plutocrats. Boris Johnson has proved that voters are quite willing to elect someone who has frequented both Eton College and Oxford's Bullingdon Club.

What does threaten Cameron is not the posh factor but the tosh factor. Successful party leaders provide a narrative for their party: a narrative that we can both understand and believe. In their prime, both Margaret Thatcher and Tony Blair succeeded triumphantly. Cameron's early attempts to follow their example have crumbled. In opposition he was actually been rather good at telling a story rich in ideas and full of pithy phrases: 'big society', 'all in this together', 'vote blue, go green'. After two-and-a-half years in office, the electorate's interim verdict is grim. He may still think of his ideas as nectar; to the wider public they now look like snake oil.

Few things would do Cameron more damage than to be regarded as a shallow, sloganising leader of a dithering and incompetent government. Unless he changes his and his ministers' ways, that is the reputation that could sink them at the next election.

See the full YouGov / Sunday Times results here

See the full YouGov / The Sun survey results on Ed Miliband's speech at the Labour party conference here

Follow Peter Kellner on Twitter: www.twitter.com/@YouGov