George Osborne has come under fresh pressure to halt controversial cuts to tax credits as new research shows that 71 Tory MPs in marginal seats could be vulnerable to a backlash from families hit by dramatic falls in their incomes.

The impact of the cuts, which will leave 3.2 million families worse off by an average of £1,300 a year from next April, is already causing concern among Conservative MPs and ministers, who believe they will punish precisely the kind of working families David Cameron claims to represent. The effects on individual households was brought home to millions of television viewers on Thursday when working mother Michelle Dorrell, who voted for the Conservatives in May, made an emotional attack on Cameron during BBC1’s Question Time, saying that she worked “bloody hard” and already struggled to pay her bills. She said Cameron had promised not to cut her tax credits but had then gone back on his word.

The electoral danger to the Conservatives is also laid bare in research released by Labour ahead of a Commons debate on the issue on Tuesday. It shows that 71 Tory MPs, including 23 new members of parliament in marginal seats, have more families who are set to lose substantial sums than was the size of their majority last May.

The House of Commons library has found that some families could lose up to £3,000 a year if the tax credit cuts are not reversed. Expert analysis for the Observer shows that in a two-child family with two parents working full-time, both parents would need to earn £9.55 an hour in 2016 to reach the same standard of living they would have had when earning the minimum wage of £6.50 in April 2015.

The issue has united Labour MPs after the first fractious weeks of Jeremy Corbyn’s leadership. Seema Malhotra, Labour’s shadow chief secretary to the Treasury, said: “These [Tory] MPs face a clear choice on Tuesday – they can either join the many families and charities speaking out about these unfair cuts or vote to give thousands in their constituencies a cut in household income of an average of £1,300. Hard-working families who are set to be affected will be watching.”

The Treasury remains adamant that it will not back down over the cuts – part of Osborne’s £12bn assault on the welfare budget. It says low-income families will be helped by a rise in the minimum wage to £7.20 an hour from next April and subsequent rises to £9 by the end of the parliament.

However, economists maintain that the rises in wages will not go anywhere near far enough to compensate for the loss of income from tax credits for millions of families, including those with children.

Rachel Reeves, formerly shadow chief secretary to the Treasury and now a member of the Treasury select committee, has rallied behind Labour’s opposition to cuts in tax credits and suggests in an article for the Observer that ministers should at the very least halt the plans for two years in order to carry out a full assessment that would demonstrate the devastating effects on millions of families. “I have campaigned for a higher minimum wage, and more employers should be paying a proper living wage. But to accompany a higher minimum wage with the largest-ever cuts to family incomes is cruel and perverse, and we must oppose them,” she says.

Tory MPs including Boris Johnson have made known their concerns. Stephen McPartland, the MP for Stevenage, who won a majority of 4,955 at the general election but has 5,900 families with children in his constituency who claim tax credits, said he believed the prime minister would now recognise the need for a rethink.

“The tax credits system is hopelessly complex and needs reform but we should be backing those who get up and go to work for low wages instead of living on welfare. The national living wage and changes to income tax thresholds will not offset enough of their loss and they will struggle to earn more money. They need our support and should be rewarded by a welfare system that is fair and helps them move forward in life.

“I am convinced that the prime minister will now recognise that we must at least mitigate the effect these changes will have on some families and that these are the forgotten voters that Labour has left behind.

“These are the families who we should be reaching out to as these are the families that are trying to work their way out of poverty and need our support.”

While some Tories are expected to voice serious concerns about the policy on Tuesday, few if any are expected to rebel on what is a Labour motion. Instead Osborne is likely to come under sustained pressure behind the scenes to act in his Autumn statement next month.