One senior right-winger said Mr Major was 'exhausted and resentful. I think he's a very nice man who's incapable of being an effective leader. He has no appeal based upon dogma. If he ceases to be successful what is there to bind the troops together?'
Repeating misgivings that Mr Major had missed an opportunity to prune away dead wood in the reshuffle, another leading right-winger said: 'It would not surprise me if John Major was not our leader come the next election.'
But other MPs rallied to support Mr Major after Lord Rees-Mogg, the Times columnist and former editor, suggested that Kenneth Clarke, the Chancellor, should move into No 10 without delay.
Sir Ivan Lawrence, the right-of-centre MP for Burton and chairman of the Commons home affairs select committee, said the suggestion was ridiculous. 'The nation has only just elected him as prime minister. It's too early to make that kind of judgement.'
Sir Keith Speed, the MP for Ashford who led the Tory mini-rebellion over railcards for pensioners after privatisation, called the suggestion 'potty'.
Mr Major will seek to reassert his authority this weekend in a speech to the Tory party women's conference emphasising the need to unite around core Conservative principles. But once again, worries on the party right about his leadership, the limited reshuffle last week and increases in direct taxation have surfaced.
Next year's European Parliament elections and by-elections, rather than the more immediate Christchurch by-election, will be crucial indicators to Mr Major's fate. If party support is not won back, senior backbenchers - and possibly some ministers - will feel moved to openly express misgivings and set in train a leadership contest next autumn.
Some MPs emphasised yesterday they did not believe that would mean a walkover for Mr Clarke, the man shuffled by Mr Major into the position of principal challenger.
For some, Michael Howard, the new Home Secretary, would be a contender. 'But a great deal will depend on how they and other ministers perform over the coming year,' one said.
For some, support for Mr Clarke would depend on him cutting back strongly on public spending and confining any tax increases to the margins, leaving income tax intact - a combination that might prove difficult to deliver.
Mr Howard would have to, as one put it, 'close his ears to the penal establishment in the Home Office' and come forward with a populist programme for curbing crime.
There was an air of disillusionment with the Prime Minister. 'Backbenchers don't wish him ill. They just have their doubts about him and are waiting to be convinced.'