Governing parties seldom commit suicide. Their deaths are usually gradual and painful. That is both why the Government will not lose the key Commons vote next week on the abolition of the 10p starting rate of income tax and why the affair is so damaging to Labour – as the party will no doubt discover in the local elections on May 1.

The stakes are high. Carrying a Budget through the Commons is crucial for any government. Defeats do occur: in the late 1970s on raising income tax allowances in line with inflation, and in December 1994 on the extension of VAT on fuel and power. The latter highlighted the erosion of John Major’s authority, but was easily offset in revenue terms.

But retaining the 10p rate would cost £7.4 billion this year, rising to £8.8 billion next year. That gap cannot be filled easily or quickly. Both Labour critics and the opposition parties are wary of backing a total reversal because of this cost. Hence the talk is of special arrangements for the fifth of households, or five million people, who lose, mainly single adults under 25, childless couples and retired women in their early sixties. Working families and pensioners gain considerably from the changes.

The Tories want to cause maximum embarrassment for Labour while not threatening their own reputation for fiscal responsibility. Hence George Osborne has said, disingenuously, that if the Government is defeated he is happy to work with ministers on alternatives.

However, any defeat next week would be humiliating for Gordon Brown and Alistair Darling. It would not only knock away a central plank of their budget strategy, but it would threaten their own survival as the resulting disarray could cause a wholesale Labour rout on May 1.

That is why government whips are correct to treat the vote as tantamount to a confidence issue. Defeat could undermine fatally Mr Brown. It could trigger a collapse of confidence leading to his replacement as Prime Minister, though not to an immediate general election, even if it only postponed a Labour defeat.

Merely setting out this possibility explains why it will not happen. Labour MPs want to use their leverage over the next week to secure more concessions from ministers – going well beyond the extension of the poverty inquiry announced last night by Yvette Cooper, the Chief Secretary to the Treasury. But Labour critics will not want to be blamed for defeating the Government before the elections.

So we are in for the politics of bluff, brinkmanship and reassurance. Until a few days ago, Mr Brown did not seem to appreciate the depth of grassroots Labour feeling, though he certainly does now, to judge by his comments to Labour MPs last night.

But finding a solution will not be easy. The Budget cannot be rewritten and, as the Institute for Fiscal Studies has pointed out, helping the various categories of losers could be complicated and expensive and depend on the take-up of tax credits. In the longer term the best solution would be to increase the starting threshold for income tax.

Even if, as is probable, the Government muddles through, the political cost will be large. Many people – core Labour voters, activists and MPs – are unhappy, and disillusioned with Mr Brown.

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