David Cameron's plans to end housing benefit for under-25s look set to be omitted from George Osborne's autumn statement this week after a Lib Dem revolt against more draconian benefit cuts.

Government sources suggested that the idea, floated by the prime minister in June as a way to trim a further £2bn off the benefits bill, has been fiercely opposed by the Lib Dem leader, Nick Clegg, and the Treasury chief secretary, Danny Alexander.

In another sign of wrangling between the coalition parties before Wednesday's statement, plans by Osborne to announce a freeze on all working-age benefits have also run into intense Lib Dem opposition.

It is expected that while Osborne will move to slash the benefit bill by several billion, he will stop short of an outright freeze after strong Lib Dem objections.

Last night Greg Mulholland MP, who co-chairs the Lib Dems' work and pensions policy committee, said his party accepted the need to make further savings where possible but there were "red lines" it would not allow to be crossed.

"The Lib Dems would not stand for cutting housing benefits for under 25-year-olds which would not only be unjust and unfair but would have unacceptable consequences for many young people. Neither do we think a freeze in working-age benefits is acceptable.

"Having spent the last year making sure that benefits are directed to those who really need them most, a move to cut them now in real terms is not the right thing to do."

The Lib Dems have said they will only allow further reductions in benefits if these are balanced against taxes on the wealthy. Osborne is expected to announce new restrictions on pension tax relief for high earners.

An Opinium/Observer poll finds more than half of voters (53%) believe cuts to welfare spending have gone far enough. Just 29% believe they should continue to be cut.

Welfare poll Photograph: guardian.co.uk

The coalition has raided the welfare budget repeatedly since 2010, with Osborne announcing that benefits would rise in line with the CPI measure of inflation instead of RPI, which tends to be around a percentage point higher.

In last year's autumn statement, the chancellor also announced a freeze on some welfare payments, including the child element of the child tax credit, while higher earners are due to lose their child benefit from April next year.

Osborne warned in this year's budget that the cost of benefits would need to shrink by £10bn a year by 2016-17 to keep his deficit-cutting strategy on track.

He will use his statement to insist that Britain is on "the hard road to recovery", despite being forced to slash forecasts for future growth, and announce deep cuts to the welfare budget.

In March, the independent Office for Budget Responsibility expected economic growth of 0.8% for 2012, but when it publishes its latest snapshot of the economy alongside the autumn statement it is likely to project GDP growth of close to zero. Next year's forecast, for 2% growth, also looks wildly optimistic, with the independent consensus just above 1%.

The economy's weaker-than-expected performance, against the background of recession and financial crisis in the eurozone, has pushed Osborne's deficit-cutting strategy way off course. He had already extended his austerity plans to 2016-17, beyond the next election, but is widely expected to add at least another year of cuts on Wednesday.

Most City analysts also expect him to break the self-imposed rule that said the national debt should be falling by 2015.

Despite the fragile state of what Sir Mervyn King has called the "zigzag" economy, Osborne will repeat his mantra that there is no alternative to stringent spending cuts.

A Treasury source said: "While it was always going to be a hard road to recovery and it may be taking longer than we hoped to put things right, Britain is on the right track and turning back now would be a disaster."

The chancellor will unveil a package of measures aimed at boosting growth, including £1bn in taxpayer-backed guarantees for small firms hoping to break into overseas markets, and more details about a state-backed business bank championed by the business secretary, Vince Cable. The government has pledged to double exports, to £1tn a year, by the end of the decade.

"We'll be showing at the autumn statement that we are serious about being one of the winners in the global race," said the Treasury source.

Osborne also backs Lord Heseltine's proposals for handing over up to £50bn in funding for skills and growth to grassroots local economic partnerships, to kickstart a regional renaissance. But government insiders say talks to implement Heseltine's blueprint have descended into a "Whitehall bunfight", with some ministers reluctant to relinquish control of the purse-strings.