Rishi Sunak has been warned against fighting an election on an unfunded plan to abolish employee national insurance amid projections the move could blow a £40bn hole in the public finances.

As the pre-election battle on the economy between the Conservatives and Labour intensified, the prime minister was on Thursday under mounting pressure to explain how the measure could be afforded while public services were crumbling.

After placing a 2p national insurance cut at the centre of Wednesday’s budget – funded through higher government borrowing, stealth tax rises and a squeeze on public spending to come after polling day – his chancellor, Jeremy Hunt, said the Tories’ ambition was to scrap the tax on workers entirely.

The modest scale of the giveaways in the budget has made a snap election less likely, although Sunak refused to rule out the possibility in interviews after the budget.

The country’s leading economists questioned how abolishing employee national insurance contributions (NICs) could be afforded without further dismantling already stretched public services, and while the next parliament was on track to be the toughest for more than 80 years for a chancellor wanting to bring debt down.

In scathing remarks for the government, the director of the Institute for Fiscal Studies, Paul Johnson, described the pledge as “not worth the paper it’s written on unless accompanied by some sense of how it will be afforded.”

The measure would cost more than £40bn a year in forgone revenue for the exchequer, he said, as the most expensive item in a list of unfunded Tory promises, including a promise reiterated in Wednesday’s budget to increase defence spending by £10bn.

The government has also refused to spell out in detail its plans for public spending after the election, beyond saying it would push for an efficiency drive alongside a 1% real-terms funding increase for Whitehall departments – a level the IFS said implied cuts of about £20bn for non-ringfenced areas outside health, education and defence.

Sunak declined on Thursday to say how the plan might be funded, telling broadcasters instead: “I think what people can see from me, I think they trust me on these things, is that I will always do this responsibly.”

The prime minister’s spokesperson also declined to say whether the government was considering forgoing the entire revenue from national insurance, or whether it was considering getting rid of national insurance by merging it with income tax, which might result in income tax having to rise.

The IFS included Labour in its broadside against the pre-election tax and spending plans being floated by both political parties. “The government and opposition are joining in a conspiracy of silence in not acknowledging the scale of the choices and trade-offs that will face us after the election,” Johnson said.

“They, and we, could be in for a rude awakening when those choices become unavoidable.”

Labour tried to deflect criticism of its own plans by turning up the pressure on the prime minister and the chancellor, saying their ambition on national insurance would come with a higher price tag than Liz Truss’ ill-fated £45bn mini budget package. It said the plan would cost £46bn a year, equivalent to £230bn over the course of a five-year parliament.

Darren Jones, the shadow chief secretary to the Treasury, said in a letter to the prime minister: “Just like Liz Truss, you have so far refused to set out how you are going to pay for this latest shake of the magic money tree.”

Casting its verdict on the chancellor’s budget, the IFS said there were billions of pounds worth of unanswered questions in the Conservatives’ tax and spending plans, including how the party would find vast savings from Hunt’s new public sector productivity drive after more than a decade of austerity.

Despite cutting employees’ national insurance by a third in the budget and in November’s autumn statement, from 12% to 8% of earnings, it warned Britain remained stuck in a situation where the overall tax take would reach the highest level since 1948 and still not make a meaningful dent in bringing down the national debt.

Amid almost two decades of falling real wages, Torsten Bell, the chief executive of the Resolution Foundation, said household disposable incomes, after adjusting for inflation, were poised to fall by 0.9% between 2019 and the end of 2024 – “the first parliament in modern history to see a fall in living standards”.

Pensioners and high earners were the biggest losers, Bell said. The idea that tax cuts could be afforded at a time when public services were faltering was a “fiscal fiction”, he added.

Hunt defended his budget, saying he wanted to “make a start” in cutting taxes to boost households’ living standards, although he admitted: “I’ve never said for one moment that I can bring them right down all in one go.”

The IFS said that by accepting the 2p budget cut in national insurance that Labour would “make life more difficult for itself” to balance the books, having lost £10bn that could have otherwise been spent on public services.

Rachel Reeves, the shadow chancellor, suggested Labour could find savings from elsewhere to fund its spending plans.

The party had planned to use money raised from abolishing the non-dom tax regime and an extension in the energy windfall tax for a number of schemes designed to elevate its spending above Tory proposals, including opening breakfast clubs in all primary schools and funding more out-of-hours doctors and dentist appointments.

However Hunt himself raised those taxes on Wednesday and used them to pay for cuts to national insurance, which Labour is backing.

Reeves told the BBC on Thursday: “We will identify the savings we can make to fund this.” Labour officials said Reeves’ team is finalising the details of what they will cut, and plan to make an announcement imminently.

Johnson said it would not be difficult for Labour to find the money to replace the £4bn a year the Tories had raised through changes in the non-dom rules and energy taxes, which were now earmarked for tax cuts.

However, Reeves’ promise to match the Tories’ tax cutting plans while pushing for savings from existing budgets sparked anger from some on the Labour left. Kate Dove, the co-chair of the leftwing Momentum campaign group, said: “It is absolutely shameful that the Labour leadership appears to be committing to further austerity in government.”