The Conservative Party is running out of ways to be liked. David Cameron is much prefered to Ed Miliband as a leader; George Osborne is trusted to run the economy more than Ed Balls. But there remains a stubborn cohort of voters, around 40 per cent, which refuses even to countenance the idea of voting Tory. This is the sticky residue of the "nasty party" label that no amount of scrubbing away at the brand seems to shift. It is the presumption shared by millions of people that the Conservatives simply aren't for the likes of them.

The resilience of this prejudice is weighing on the party's strategic minds. Andrew Cooper, Downing Street's resident pollster, has surveyed the land for deposits of potential support to be mined. In a recent presentation at a party away day, he highlighted voter reserves in urban constituencies in the north of England. Wales presents a few opportunities. Scotland is a write-off.

Meanwhile, Conservative MPs have been instructed to befriend their local minority-ethnic communities. They have also been reminded to avoid sounding like flint-hearted actuaries when explaining that painful measures are necessary to control the Budget deficit.

The harder it gets to imagine a great surge of affection for the Tories, the more emphasis they place on the policies that do enjoy mass support. Above all, that means faith in the talismanic power of benefit cuts.

Reductions in the welfare budget of £18bn will leave millions worse off. Ordinarily, such a brazen raid on the pockets of the poorest citizens would damage a political party. The Tories can do it because enough people are persuaded that the money represents the last government's subsidy for idleness and an affront to anyone who works for a living.

If the cap fits

Labour is losing this argument and knows it. The government's plan to cap the amount any household can receive at £26,000 – roughly equivalent to an average family income – is especially popular. Many would have the cap much lower. As one shadow minister put it to me, shortly before voting against the measure in parliament: "The only thing my constituents are taking out of this debate is: 'Wow! Can you really get 26 grand on benefits?'" (You can't. The highest payouts are for housing benefit in London, which goes straight to landlords, although that is hardly a more defensible subsidy.)

George Osborne, Cameron's election strategist as well as his Chancellor, is convinced that benefit-bashing has little or no downside. Even when the government encounters resistance to its plans – as recently over a scheme that prodded benefit claimants into unpaid work experience – the message gets across that Tories aim to turn slackers into strivers.

But the effectiveness of that message relies on two promises. First, there will be jobs for those that seek them. Second, welfare will be reformed so it is always more lucrative to work than to sign on. Both propositions look shaky.

Intractable unemployment is already threatening to derail the Work Programme, a vast scheme under which the Department for Work and Pensions (DWP) uses private companies and charities to place people in jobs. The service providers are paid according to how effectively they steer their "customers" off benefits. Many complain in private that labour-market conditions are making their contracts unviable. A high-profile bankruptcy or an embarrassing government bailout looms.

Meanwhile, the Universal Credit, Iain Duncan Smith's grand project to simplify the benefits system and eliminate perverse disincentives to work, is bogged down in technical difficulty. It was initially conceived as the Work and Pensions Secretary's moral crusade against welfare dependency. It is a labour of love. Unfortunately, love can't commission the complex IT system required to integrate a sprawling mass of disparate entitlements. Nor can it manage relations with the Treasury and local government, without whose co-operation a unified benefits system is impossible.

There is a growing feeling across Whitehall that Duncan Smith and the DWP are bungling the operation and that an October 2013 deadline for delivery looks wildly optimistic. The likeliest outcome is what one senior official describes as "the existing benefits system, slightly tweaked, with a blanket thrown over it".

Off the rails

There is, in other words, no welfare revolution, just cuts. The impact will be felt increasingly by people who have jobs but rely on benefits to stay in their homes, and people who are disabled or chronically ill. Persistent unemployment will make it harder to accuse those who can't find work of not looking hard enough. Shock at a rise in homelessness and conspicuous poverty will make demands on the nation's conscience that compete with confected rage at Labour's spending legacy.

That doesn't mean the opposition will start winning arguments on welfare. Labour needs to have a line before it can defend one. It does, however, seem likely that the high point of public enthusiasm for the Tory position is now. There is a nasty edge to Conservative language around benefits. It is meant to be balanced by the compassionate impulse behind Duncan Smith's reforms, but good intentions cannot stop the IDS train from leaving the rails.

What then will make the Tories liked? The limitations on the party's electoral prospects have been camouflaged by success in controlling the terms of economic debate. The question of whether people like being governed by Conservatives has been subsumed by the argument that, given Labour's supposed vandalism of the public finances, no credible alternative exists.

Cameron more or less admitted that much in a speech to the party faithful on 3 March. "True compassion isn't wearing your heart on your sleeve," he said. "It's rolling up those sleeves and taking the long-term decisions that will really change our country for the better."

Unable to persuade the public that the Tories can be nice, Cameron is forced to offer nasty in the national interest. It is a proposition that failed to win a majority at the last election. There is no obvious reason why it should work better next time.