A defeat for the Tories in the Christchurch by-election on Thursday will come as a further blow to Mr Major's authority.
Lord Tebbit, the former party chairman, confirmed that there were some who wanted to change Prime Minister, but were worried about the successor. He said Mr Major faced 'hazards' over his leadership at the party conference, the Budget and the European elections.
Some Tory MPs believe he may stand down next year, if the party's fortunes have not improved. But the prospect of Mr Major being replaced by the more pro-Maastricht Kenneth Clarke, the Chancellor, has alarmed the Thatcherites.
'If not John Major - who?' Lord Tebbit, former Tory MP for Chingford, said. 'His difficulties are not primarily about Maastricht. They don't talk in the pubs in Chingford about Maastricht. They talk about the economy . . . The real problem for those who would like a change is a change to whom?
'Just as in the vote of confidence, the strength the Prime Minister had was that no Conservative MP wanted to rush into a general election when the Prime Minister's and the Government's ratings were at an all- time low, similarly, people are not anxious to have another wounding and damaging party election unless there is a clear candidate on whom they could all agree.'
He said that in some ways the party was suffering from the wounds caused by Michael Heseltine in bringing down Baroness Thatcher. 'You don't want to do that again. It would be a terrible mistake. Look what happened in the past. The Macmillan failures - Alec Douglas Home followed. In no time at all, the party was dissatisfied. What did they do? They landed with Edward Heath, who all but destroyed the party.'
The party did not want another 'coup d'etat', Lord Tebbit said. Mr Major had to take the rebels over Maastricht along with him and that might mean 'some sacrifices' - a view echoed Lord Parkinson, another former party chairman.
However, Sir Edward Heath and Lord Howe warned Mr Major at the weekend against appeasing the rebels. 'There is no future for John Major if he continues to seek compromise with a group of people for whom the word has no meaning,' Lord Howe said on BBC radio.