Workers of the world, unite. Nothing’s too good for the workers. You know what it means, instantly, when you see “worker” in a phrase like that – what kind of working people, exactly, is being addressed.

You know it doesn’t mean billionaires, even if they spend every waking hour in the office. It doesn’t mean people who own a string of buy-to-lets either, no matter how long they spend managing their property empire. Conversely, you can identify as working class in this sense even if you’re currently not actually doing any work but are on strike, or looking after small children, or even retired. Being a worker is more a virtuous state of mind than a socioeconomic definition, and like all feelings it doesn’t always make logical sense. But when wrapped inside a clear political ideology, somehow it works.

So it’s easy to see why the self-proclaimed party of the working classes thought it was being clever in its manifesto by talking about not raising taxes on “working people”. The implication wasn’t just, as Labour now insists, that it wouldn’t raise headline taxes on wages (for a start it also covered VAT, paid by workers and non-workers alike). It was more that if taxes had to go up, it wouldn’t be you who got whacked: it would be some ill-defined other guy, who definitely deserved it. Like Theresa May’s “just about managings” or Ed Miliband’s usefully vague “squeezed middle”, Keir Starmer’s “working people” was a generous elasticated waist of a label stretching to fit almost anyone minded to squeeze into it. The budget, however, is the moment that elastic snaps.

Cabinet minister after cabinet minister has struggled to define who, exactly, is a “working person” and therefore on the side of the angels come Wednesday. Starmer’s own effort – someone who “goes out and earns their living” and can’t just “write a cheque” to get themselves out of trouble – was rooted in what the Labour party has historically meant by a worker, despite sounding faintly antiquated. (What if you stay in and work from home? When did anyone last write a cheque?) But it only begs further questions, especially for self-employed people and those scraping by.

The education secretary, Bridget Phillipson, wouldn’t say at the weekend whether owning a small high-street hairdresser’s – being on your feet for 10 hours a day, poring over your accounts of an evening, all for a net profit of £13,000 a year and now the potential threat of higher employer’s national insurance contributions – made you the right kind of “working person”. But being prime minister apparently does, even though Starmer is paid more than 10 times that figure and owns a house worth a reported £2m, because as Rachel Reeves explained: “He gets his income from going out to work.” If you’re the hairdresser, how is that fair? When Pat McFadden, arguably the cabinet minister closest to Reeves’ and Starmer’s thinking, was asked on Monday morning who counts as a virtuous “striver”, he told the BBC: “We’re not talking about picking out one set of people or another.” But unfortunately that’s exactly what a budget always does, which is why this row is about more than linguistic nitpicking. At heart it’s about who this budget – and by extension this government – is for.

Starmer’s manifesto promise that “Labour will not increase taxes on working people, which is why we will not increase national insurance, the basic, higher, or additional rates of income tax, or VAT” was crafted with lawyerly provision to reassure swing voters, while still leaving Reeves just about free to raise billions by other means. But if the letter of it was very specific, the spirit conveyed was that “working people” – average Joes on modest incomes who don’t have complex tax affairs, children at private school or a second home they rent out on Airbnb – would be spared while broader shoulders took the hit. The manifesto raised progressive hopes, in other words, while simultaneously ruling out the most obviously progressive mechanism of just raising income tax. What we’re seeing now is the messy process of Labour trying to square that circle.

Once the budget lands, what will matter most isn’t litigating the precise meaning of a manifesto pledge most people never read, but how closely the country feels it has stuck to that spirit. If what emerges still broadly resembles what many Labour voters thought they’d be getting, namely a package that favours the little guy over the fat cat, then the chancellor will have done her job – given the state of the country, polling shows most voters who switched to Labour in July would still rather have better public services than lower taxes and are willing to take some short-term pain so long as it feels fairly distributed. But if it doesn’t feel fair, then the dispiriting lesson many will take is that the cynics were right and politicians aren’t to be trusted. And that’s far more corrosive, in the long run, than a few angry landlords.

• Gaby Hinsliff is a Guardian columnist