Change*. If Labour’s one-word campaign slogan had an asterisk, it would have directed voters to Rachel Reeves’s budget.

Later this month the chancellor will attempt to walk the line between repairing Britain’s battered public realm, while sticking to a manifesto promise to balance the books without raising taxes on working people.

However, as the Institute for Fiscal Studies warns in its pre-budget analysis, this leaves Reeves with the job of financing change within tough constraints of the party’s own making. It’s a challenge that could be tough, it says, if not impossible to unpick without moving the goalposts.

Part of the difficulty stems from the chancellor’s inheritance from the Conservatives.

First of all, taxes are at a historical high, debt is at the highest level since the early 1960s and forecast to only barely decline in five years’ time. In addition, many public services are under strain – driving up Britain’s spending needs. The previous government struggled with this, to the point Labour claims the Tories left £22bn unaccounted for in the current financial year.

Meanwhile, Reeves has committed to two fiscal rules – also inherited from her predecessor, Jeremy Hunt: to balance day-to-day spending with tax receipts and, second, to get debt falling as a share of the economy in the fifth year of forecasts produced by the independent Office for Budget Responsibility.

Reeves has done little since Labour’s party conference in Liverpool to quash speculation that she will relax the debt rule. This would unlock headroom to increase funding for capital investment – but not without risk as it could unsettle financial markets.

However, the IFS warns that arguably a bigger problem at the budget will be the chancellor’s other rule – to balance the so-called current budget – given the priority to repair public services, which will require a boost in day-to-day support.

Two things in particular make this challenging: the amount Britain spends on servicing its high levels of debt; and the demands of providing services and welfare support for an ageing, increasingly unwell and expanding population. Both put spending on a rising trajectory.

To match that with revenues, while having committed not to raise the three largest earners for the Treasury – income tax, national insurance and VAT – is a tough ask. That has left Reeves to focus elsewhere, in a scrabble for cash behind the sofa that is reportedly causing the chancellor some headaches.

Even after £9bn of tax rises in Labour’s manifesto – including some that are now said to be in question – the IFS reckons Reeves would only just have scope to ensure that government departments would not face real-term cuts in their budgets.

This would just about meet Keir Starmer’s promise of “no return to austerity”. But after years of cuts, and with many services overwhelmed – take the Prison Service, or asylum system as examples – it would not provide much more space to drastically improve services.

The IFS therefore argues a more realistic definition of escaping austerity would be raising departmental spending in line with economic growth – but if Reeves wanted to do this and meet her current budget balance rule, it would require an extra £16bn on top of the tax rises in Labour’s manifesto; so almost £25bn in total.

It is usual for new governments to set tough tax-raising budgets when coming to power. But a rise on that scale would be far bigger than the ones implemented by Gordon Brown in July 1997 and George Osborne in October 2010.

Much of this could be helped by securing stronger economic growth, which would drive up tax receipts and make the chancellor’s job easier. The IFS acknowledges this. But it warns this is no easy task in itself, while there are also risks of growth disappointing.

All of this leaves Reeves in a bind, with the unenviable task of finding the resources to deliver the change voters were promised.