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This ideological budget is more brutal than 1981. As the unjust distribution of pain emerges, the rebellion will resound

The dust doesn't settle, it is blowing into an ash cloud. On closer inspection, this has become the "impossible" budget. David Cameron tells the G20 that "we must each get our national finances under control", but it looks unlikely that the cuts in his red book can be achieved. That may be good news, but it suggests the axe-wielders may know alarmingly little about the public services they are hacking at.

Ask the Institute for Fiscal Studies â€" that indispensable extra arm of the British political system â€" and it admits cuts of a quarter and, in some departments, a third, can't and won't happen.

Asked by pollsters, people dutifully say the deficit is the most important problem â€" just as people used to worry about the now forgotten balance of payments. There is a genuine economic crisis, and no one denies the deficit needs to be cut. But how long will that last? They will smell a rat once they suspect this government is using the crisis as cover for other ideological ends. Why is £40bn more to be cut than was expected or demanded by markets? Why create a surplus in six years? Why shrink the state to below 40%, more than Margaret Thatcher achieved?

Cuts will only be trusted if done in a spirit of causing least possible harm to valued public services. Frugality is undoubtedly necessary, but people will turn against all cuts if they go far further and deeper than absolutely essential. Politically, it may work now to turn "gold-plated" public servants into public enemy No 1. Illustrating welfare cuts with juicy anecdotes of scrounging families may sway opinion temporarily. But Osborne, Cameron and Clegg will regret their tones of glee when the public mood changes â€" as it will. They could have squeezed out a crocodile tear.

Ministers now negotiating with the Treasury over cuts to their departments would do well to remember the fate of the former social services secretary John Moore, Thatcher's favourite, who offered up too many NHS cuts in order to please her. After two years of exceptional severity the NHS exploded, as it always does, with deaths on waiting lists and ward closures: in the crisis he was fired. Without 2%-3% extra a year just to stand still, the NHS erupts. When Labour cut it right back in the first two years, again, a winter crisis forced Tony Blair to promise a monumental spend. Even though the NHS is "protected", George Osborne plans a six-year spending drought unseen since the war: just wait for the eruption.

Consider what a one-third cut in local government will do. When a child or an old person dies and the local director of children's services says she had to cut a third of her social workers, ministers will not be able to keep the blame local. This is not exaggeration: these cases will certainly happen. New ministers, eager to please the Treasury, would be well advised to fight their corners hard in the star chamber â€" for they will be blamed for cuts that go too far.

As the unjust distribution of pain in the budget emerges, what will be the trigger for Lib Dem rebellion and public indignation? The cutting of 10% off the £65 jobseeker's allowance for anyone out of work for a year may become the equivalent of Gordon Brown's 10p tax-rate abolition. It took a year after the approval of the budget before the public realized what he did. Or will it be the realization that all the benefits of losing an additional 1% per year, each year, increasing the cut, due to changes in capacity increase of RPI (retail price index) CPI (consumer price index)?

Now it turns out that banks will probably gain more in corporation tax cuts than they lose in the bank levy, the Treasury documents show that on average businesses have been paying only 21% or less in corporation tax anyway. No sooner does the budget cut free school meals from half a million children than Ofsted research reveals too many poor families can't afford lunches for hungry children. One small shocker: among performance indicators dropped, local authorities no longer need show they are finding accommodation for young offenders released from prison. How clever is that?

There is an extraordinary insouciance about Cameron's letter to public servants asking them to suggest cuts to their own precious services. Caricatured by ministers as feather-bedded idlers, their work devalued, it is hard to believe they will be eager to turn quisling. But how the public-sector unions react to the cuts will be important. Sabre-rattling by Len McCluskey on Thursday, as he seeks election as Unite leader, doesn't capture the mood within the TUC. Strike calls against the two-year pay freeze and the probable extra pension contributions are unlikely to win public support or indeed support from union members who see jobs being cut all around them. But public sympathy may flow for strikes against job and service cuts, as armies of healthcare assistants, teachers and teaching assistants, librarians and an estimated million others are thrown out of work.

Inequality will now, without doubt, yawn yet wider again, as the distributional impact becomes depressingly clear. Many well-paid people, like myself, have now found they have been barely touched at all by the budget â€" not even my winter fuel allowance or Freedom Pass. But even the better-off will see local libraries, leisure centres and police stations closing, dirty streets and overgrown parks, fewer buses, the homeless back on the streets in 1980s numbers, rising crime and public squalor. The sense that the cuts were needlessly brutal will soon take hold.

The Liberal Democrats' problem looks terminal: all is bet on the heroic assumption that the economy comes good, growth is miraculously quick and the pain was worth it. But with high unemployment likely to be long-lasting, their voters will be unforgiving.

Labour has a grave problem: part of the deficit was Brown's fault. Can a new leader judiciously accept some blame, admit some past errors and construct a deficit reduction plan that is solidly convincing, and yet less savage?

The British Election Study by Professor Paul Whiteley of Essex University reminds us that the fallout from the Thatcher/Howe budget of 1981 was an unpopularity so profound that had it not been for the Falklands war, "Labour would have won in 1983, despite their longest suicide note in history manifesto". That budget was moderate in comparison to this one.