George Osborne is facing a battle with the work and pensions secretary, Iain Duncan Smith, over his plan to impose an extra £12bn in welfare cuts after the next general election.

Conservative sources said Osborne's intervention – a proposal that also prompted Nick Clegg to publicly warn that the chancellor is in danger of making a "monumental mistake" – had highlighted stark differences of approach between the chancellor and Duncan Smith over how to reform Britain's social security system. Osborne demanded that roughly half of future spending cuts in the next parliament come from the welfare budget.

"There is a difference in narrative between George Osborne and Iain Duncan Smith who both want to cut back the welfare state," one senior figure said. "There is the lopping off narrative of George Osborne and then there is the narrative of making people less reliant on the welfare state by making work pay. But that takes a long time."

Osborne alarmed Duncan Smith and angered Clegg when he said on Mondaythat £25bn in spending reductions, due to be imposed between 2016-17 and 2017-18, would have to include £12bn in welfare cuts. The move risks creating a cabinet row that runs beyond Monday's public spat.

Paul Johnson, the director of the Institute for Fiscal Studies, had estimated after the chancellor's autumn statement last month that such welfare cuts would have to be introduced if day-to-day government spending on departments such as the Home Office is to be reduced no further than the 2.3% a year cut that has been imposed by the coalition since 2011.

Osborne outlined the tough choices ahead when he said in a speech at the West Midlands headquarters of Sertec: "It's far too soon to say: job done. It's not even half done. That's why 2014 is the year of hard truths. The year when Britain faces a choice.

"Do we say: the worst is over; back we go to our bad habits of borrowing and spending and living beyond our means – and let the next generation pay the bill? Or do we say to ourselves: yes, because of our plan, things are getting better. But there is still a long way to go – and there are big, underlying problems we have to fix in our economy."

In an interview on Radio 4's Today programme, Osborne said he would seek to achieve some of the £12bn savings by targeting housing benefit for under-25s and by means-testing people on incomes of £60,000 to £70,000 who live in social housing. But one Whitehall source said that targeting those two areas would produce "laughable" savings. Department of Communities and Local Government figures show that the 11,000 to 21,000 council tenants, who earn more than £60,000 a year, each cost the taxpayer £3,600 a year. Targeting this group would produce savings of £40m-£76m a year.

Department of Work and Pensions figures show that 351,678 people under the age of 25 claim housing benefit at a cost of £1.8bn. Of these 55.6% of these are parents, which means the cuts would not apply to them. Osborne's plan would therefore produce savings of £827.4m in this area. But Whitehall sources suggested this figure could be reduced to as low as £50m once other groups among the under-25s, such as victims of domestic violence, are excluded from housing benefit cuts. "It is laughable that you can get anywhere near £12bn in cuts this way," one source said.

Osborne also ruled out cutting pensioner benefits, such as the winter fuel allowance and free television licences for the over-75s, on the grounds that this would only make savings of a "few tens of millions". But Carl Emmerson, deputy director of the IFS, said: "On winter fuel payments plus TV licences you get up to £2bn depending on how aggressively you means test."

Emmerson also said that David Cameron's decision to guarantee the pensions "triple lock" – increasing them annually in line with the highest of inflation, average earnings or 2.5% – would cost £15bn a year by 2050.

But Emmerson said it would be unlikely to be too costly if the economy grows – and Britain avoids a recession – in the next parliament. "The funny thing about the triple lock is that you have to increase pensions by the greater of prices, earnings or 2.5%. Over the next parliament the OBR thinks that earnings will be bigger than 2.5% or inflation every year. So therefore it costs zero [in real terms]."

As the debate intensified, Robert Chote, head of the Office for Budget Responsibility, endorsed a claim by the IFS director that Osborne's plans would mean hitting the sick and disabled. Chote told Radio 4's The World at One: "The decision to stick with the triple lock, which basically ensures that you are not going to reduce by very much the share of national income that you're spending on the state pension, means that if you want to get money out of the social security budget in total, it does have to come from the sorts of areas that Paul [Johnson] is talking about."

Clegg chose to describe Osborne's plans to target cuts on the working-age poor – while ruling out tax increases – as "lopsided and unbalanced". In a sign of how coalition relations will remain fractious until the election in May 2015, the deputy prime minister said: "You've got a Conservative party now who are driven, it seems to me, by two very clear ideological impulses. One is to remorselessly pare back the state – for ideological reasons just cut back the state.

"Secondly – and I think they are making a monumental mistake in doing so – they say the only people in society, the only section in society, which will bear the burden of further fiscal consolidation are the working-age poor."

Signalling how he will waste no time in publicly criticising Tory plans over the next 16 months, Clegg later added: "I literally don't know of a serious economist who believes that you only do it from that lopsided, unbalanced approach. Almost all serious economists say you have some kind of mix."

Clegg has agreed spending plans with Osborne for the first year after the general election and has accepted the need for fiscal tightening of £25bn between 2016-17 and 2017-18 in order to meet the target of eliminating the budget structural deficit by 2017-18.

But in a taste of what is likely to be one of the main election battles – over the means by which the deficit should be cut – Clegg said it was wrong of the chancellor only to highlight the welfare bill for cuts and said the chancellor was wrong to play down the need for further tax rises.

Clegg's remarks show the Liberal Democrat manifesto for the next election will include a "mansion tax" on properties worth more than £2m. But the Lib Dems will also include the costly "triple lock" on pensions. David Cameron said on Sunday that the Tories would guarantee the triple lock, one of the main features of the Lib Dem manifesto in 2010, until 2020.

The Lib Dem mansion tax would raise about £2bn. But Clegg said he was committed to achieving at least 20% of the £25bn fiscal consolidation – £5bn – through tax increases. This means he would have to find a further £3bn in tax increases imposed on the wealthy.