The interim Labour leader Harriet Harman was struggling on Monday night to hold the party together on welfare changes as she urged Labour MPs not to vote against the welfare reform bill, telling them this was not a good time to campaign against the public.

In the first big stumble of her interim leadership, Harman received a lukewarm response at a meeting of the parliamentary Labour party and may not be able to hold the line that Labour MPs abstain on the work and welfare bill in a vote due to take place next week.

Harman believes the party needs to send out a message to voters that it is listening to the public about its lack of trust in Labour on the economy and welfare and cannot continue with blanket opposition to the budget changes that chancellor George Osborne is introducing. She told MPs: “We cannot campaign against the public. We have got to be seen to be having a debate. We had a lot of unity after the 2010 election and maybe we should have had a bit more discussion.”

She added: “In the last period of opposition we had lots of virtuous voting,” adding the party had voted against every government welfare changes and the only resistance that appeared to register with the public mood was its rejection of the bedroom tax.

Faced by hostile response, the issue will now be discussed by the shadow cabinet on Tuesday, but at least three of the party leadership contenders have rejected her approach, whichthey regard as a lack of consultation from someone that is only holding the post until mid-September.

Harman tried to reassure MPs that she was not seeking a clause 4 moment, saying it was nonsense to suggest she was seeking any personal kudos from taking on the party, stressing she was leaving many of the key decisions to whoever succeeded her as party leader.

In a bid to mollify Labour MPs, she said the party would vote against the budget on Tuesday due to the cuts to tax credits, the dropping of child poverty targets, cuts to cutting student maintenance for poor students and the reduction of employment support allowance to the value of jobseeker’s allowance. She suggested the Labour might call for a review of the lower household welfare benefit cap, even though support for the cap had been in the party manifesto.

She said it would be for the next leader to decide if the party should oppose child tax credits being withdrawn after the second child for new families from 2017. One Labour MP, Stephen Kinnock, has likened the proposal to eugenics.

Harman said: “If you have blanket opposition to everything, it is very difficult to be effective and get a hearing for the things on which you wanted to focus your fire.”

Harman has been criticised by three of the four leadership candidates for suggesting that there is a public appetite for Osborne’s decision to limit support through tax credits and universal credits to two children.

Labour whips said they expected as many 60 Labour MPs to vote against the welfare bill in defiance of Harman’s position, a number that would probably force her to back down.

Leadership frontrunner Andy Burnham led the other candidates in calling on the party to oppose the cuts, saying that was “how Labour makes itself relevant. Labour wins when Labour speaks for everyone, for the whole and that’s what it will do under my leadership.

“You don’t allow a change that is going to take money off people in work who are trying to do the right thing.”

Yvette Cooper said the tax credits were “an important part of making work pay” for many families.

“I think we can be credible and also say we are going to oppose the things that the Tories are doing which are going to hit work and hit people’s incentives to work,” she said.

Leftwinger Jeremy Corbyn, who has set up an online petition against cuts to child tax credit, said Osborne’s budget had been “brutal and anti-young and anti the poorest in Britain”.

Liz Kendall backed the two-child policy: “People said to us ‘We don’t trust you on the money, we don’t trust you on welfare reform’,” she said. “If we are going to oppose things, we have to put something else in its place because if we carry on making the same arguments we have done over the last five years we will get the same result.

“We have to put forward a different credible alternative and Harriet was absolutely right to say that.”

Kendall said the cuts – which limit support through tax credits and universal credits to two children – needed to be accompanied by the introduction of a “genuine” living wage above that proposed by the Tories.