The Conservatives gather for their conference in Birmingham tomorrow facing a new challenge along with the mountain of more familiar ones. The fresh obstacle comes in the form of Ed Miliband's speech to his party's conference. Suddenly, Mr Miliband no longer seems the unelectable figure that the Conservative leadership had been banking on. More significantly, the contents of his speech, and the attempted capture of the "One Nation" label, present David Cameron with a dilemma that is not easy to solve.

The Conservative leader was already under pressure from the right of his party, and from Ukip. He has shown increasing signs of succumbing to that pressure, from the tax cut for high earners to his heightened Euroscepticism, and his half-hearted attempts to persuade his MPs to support Lords reform to his appointment of a climate change sceptic as Environment Secretary. But now Mr Cameron needs to pay more attention to what is happening on the other side of the political spectrum, as he did – briefly and superficially – in the early years of his leadership when he spoke of his support for "One Nation" Conservatism. The success of that early rebranding project, though, was limited.

On this basis Mr Miliband's speech might have done Mr Cameron a favour. Perhaps the Prime Minister will try to revisit the themes of his early leadership when it seemed he had glimpsed a modern, more compassionate Conservatism. He should do so; the further right he has travelled the less popular he and his party have become, creating the space that Mr Miliband has sought to occupy. But it is too late for much revisionism. The governing party's course is set by policies, not words, at a conference. Such luxury is the prerogative of the Opposition.

House of Lords reform is sunk. Electoral reform is gone. Environmental targets have been scrapped. Taxation policy is set. Vetoes in Brussels have been wielded clumsily. There is a limit to how much a leader can say in a conference speech to change perceptions when voters are making their own judgements on the basis of delivery and competence – both of which were so vividly called into question by this week's railway franchise debacle.

The context is constraining too. Over the years Mr Cameron has managed to alienate those to the left of him and those to the right. While he must address the challenge posed by Mr Miliband from the left, he still cannot entirely ignore Ukip on the right, and its attraction to his still fervently anti-European party. At the Liberal Democrats' conference in Brighton, it was the Conservative Party that was attacked more often than the Coalition's opponents, as MPs and activists stepped up their "differentiation" strategy in relation to their governing partners. At mid-term in a hung Parliament the Conservatives are more beleaguered than at any time since Mr Cameron became leader at the end of 2005.

The Prime Minister can cling to some straws. Among business leaders, as our poll shows today, he still leads Mr Miliband in terms of personal ratings. Almost certainly the economy will be growing again by the time of the election. The Liberal Democrats show no sign of wanting to pull out of the Coalition. All three are significant positives but they afford only limited comfort.

Mr Cameron does not deserve to carry all the blame for his party's overall unpopularity and restiveness. But he has been leader for nearly seven years now without ever seeming entirely authentic or clear about why he is in politics. This week gives him another opportunity for definition. He should attempt it by tackling Ed Miliband and his One Nation claims, rather than by further appeasing those on his right.