Even more unexpected than the European Union winning the Nobel Peace prize, the winner of the party conference season is … David Cameron. This was the paradoxical result of Ed Miliband making a speech that most of its audience found impressive. A few of us were, I admit, unmoved by the amazing feat of walking and talking for 65 minutes without much hesitation, repetition or deviation, but the rave reviews for the Labour leader saved the Prime Minister by forcing him to respond.

Cameron's speech was defensive, devoted to an unusual extent to rebutting the charge that he was a posh boy who went to a posh school and therefore could not represent "one nation". But it was also the chance, for which he had been waiting, to move his party back to the centre after the rightward drift of the past six months.

You did not have to agree with it to recognise that Cameron's speech was a rehearsal of powerful arguments that are more likely to persuade undecided voters than Miliband's empty rhetoric.

For all the difference they made to this month's opinion polls, the parties need not have bothered with annual conferences. Miliband's personal ratings edged up from the depths of contempt, so that he is now only slightly more unpopular than Cameron. But the Labour lead is within the margin of error of the nine or 10 points it has been since the Budget. Few people pay much attention to mid-term political speeches. Yet they tell us a great deal about how things may play out when the battle is eventually joined.

In his speech, Cameron finally engaged with exhibit A, adduced in evidence by Miliband the week before: the cut in the top rate of income tax that will take effect next year. The moment it was leaked by the Liberal Democrats before the Budget in March, this tax cut for the rich has seemed to be the biggest mistake made by Cameron and George Osborne so far. At a stroke, it undercut the language of shared sacrifice and "all in it together".

The Prime Minister was helped by Miliband's suggestion that the tax cut would take the form of a cheque written by HM Revenue and Customs to "millionaires", including Cabinet ministers. That allowed Cameron to turn the debate to Miliband's apparent failure to understand that money raised in tax belongs to the taxpayer.

"Let me explain to you how it works," said Cameron, referring to his opponent by name, something a prime minister usually avoids doing for fear of conceding equality of status. "So if we cut taxes, we're not giving them money – we're taking less of it away."

It was not a whole answer. The symbolism of a tax cut for people on incomes over £150,000 remains awkward. And there is still a tension between the Tories laying claim to "aspiration" and their pointing out, as George Osborne and Cameron both did in their speeches, that "the rich will pay a greater share of tax in every year of this Parliament than in any one of the 13 years under Labour".

However, it is clearer now how the Conservatives will fight on the central ground of the economy and the public finances, even if growth remains disappointing. It is no use Ed Balls protesting that more borrowing now might actually reduce borrowing in the longer term. The Tories will simply repeat Cameron's line: "Labour: the party of one notion – more borrowing." All Miliband and Balls can do is promise to stick to Tory spending plans, and hope that the folk memory of their splurge-and-bust will fade.

Cameron also had a response to the other perception of Tory weakness: that he and Osborne have no programme except cutting the deficit. The welfare section of his speech tied a popular policy that Miliband won't match – capping housing benefit at the level of average workers' earnings – to a "responsibility" message. Again, workable welfare reform is complex and expensive, but the details are trumped by Labour putting itself on the side of recipients rather than of taxpayers who fund it.

Then, on schools, Cameron performed the truly extraordinary feat of presenting himself, an Old Etonian, as a better and more authentic champion of the right of the many to the quality of education currently available to the lucky few. While Miliband pretended to be something he is not, a struggler who had survived his comprehensive school of hard knocks, Cameron walked off with Tony Blair's aspiration of "independent state schools for all". Left-wing commentators with tin ears wailed about the "oxymoron" of "spreading privilege", deaf to how it might be heard by less ideological or pedantic parents.

That is what the argument is going to be at the general election. The party of balancing the books, of responsibility and aspiration, on the side of taxpayers and parents who want the best for their children, against – well, what?

The only question is how much the Conservative Party will do to destabilise its leader, who is its best hope of holding on to power. The first test is to avoid a nervous breakdown after the Corby by-election and police commissioner elections on 15 November.

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