Signs of the next wave of difficulty came almost immediately, however, with a call for a rightwards Cabinet reshuffle in advance of widely anticipated poor results in May's council elections and June's European elections.
While Lord Tebbit, the Thatcherite former cabinet minister, accused the Government of 'serious errors', the message from the centre-left, whose favoured candidate, Kenneth Clarke, is battling against a bad Budget press, was that it was better to keep Mr Major as Prime Minister - even if he went on to lose the next election - than to have a damaging leadership contest.
Amid reminders of his uncompromising handling of the Maastricht rebellion, the belief is growing that that Mr Major would not 'go quietly'. A Conservative Central Office source said: 'His stamina and courage have been consistently underestimated. He has time on his side. He will lead us into the next election. He is nobody's pushover.'
Central Office insists that in contrast to 1990, with the fall of Margaret Thatcher, the demise of the Prime Minister would not have a profound effect on the party's fortunes in the opinion polls.
But despite the entreaties of ministerial supporters, the debilitating war of attrition with Labour, the right of the party and a largely disenchanted Tory press is set to continue, with right-wingers quick to emphasise yesterday that they had been instrumental in Mr Major's leadership victory.
John Townend, a right-wing executive member of the influential 1992 Committee and chairman of the backbench finance committee, set out an uncompromising list of demands for the Prime Minister: squeeze public spending further, cut out waste, increase efficiency, reduce manning and use the savings to reduce tax.
Calling for a major Cabinet reshuffle in the next two or three months to avoid claims of post-election panic, Mr Townend said: 'We need to see a government in this reshuffle more representative of the centre-right.'
Lord Tebbit likewise told ITV's Walden programme that while he very much favoured Mr Major staying, the key problem of tax arose out of public spending. The only person who had fought it at all effectively was Baroness Thatcher.
At times damning Mr Major with faint praise, Lord Tebbit said: 'What he does need to do is . . . determine very very clearly indeed where he wants to be by the end of this year, what he wants to have happening, what message it is that he's giving to the British public . . .'
In an apparent criticism of Sarah Hogg, head of Mr Major's policy unit, and her staff, Lord Tebbit also claimed 'very poor staff work' had failed make 'back to basics' more than a slogan, and proof against attack.
Warning against a leadership contest the centrist Sir Geoffrey Johnson Smith, a 1922 Committee vice-chairman, said: 'What really matters in the end is whether your policies succeed. What also matters is, is there someone who stands out above everyone else as the most desirable person who can lead you out of the wilderness? There isn't such a person.'
There is growing Tory opposition to the local government commission's proposals to replace the two-tier council structure with unitary authorities. Opposition is most marked in the West Country and Yorkshire, where the commission has made most progress.
David Heathcoat-Amory, MP for Wells, who is also Minister of State at the Foreign Office, said last night: 'All four Conservative MPs in Somerset are against the proposals. The commission has made a mistake. Their proposals are bad in structure and unpopular.' Eight other MPs are likely to defy the Government over the proposals.
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