The MP for Tatton, who is protesting his innocence in the Commons cash- for-questions affair, is most unlikely to volunteer to stand down.
However, the intensity of party pressure is becoming so great that Mr Hamilton's local party association could well crack and refuse to adopt him as its candidate.
The problem for the Conservatives is that the sacrifice of Mr Hamilton would not kill the debilitating furore over sleaze, which has derailed John Major's campaign plans.
A senior Labour source said last night that once Mr Hamilton had been ditched, they would turn their fire on Michael Brown, another MP accused of accepting cash from Mohamed al-Fayed, the owner of Harrods.
Following last week's appeals from the party hierarchy, the pressure for a purge came yesterday from the Tory backbenches, with John Townend, a member of the party's backbench 1922 executive committee, saying: "Sometimes we have got to sacrifice our own position for the greater good."
He told BBC radio's The World this Weekend: "There is such a lot of upset throughout the country amongst our party workers, they wonder what on earth is going on, and as somebody said earlier, we have got to lance the boil."
Mr Townend, who had been put forward for interview by Conservative Central Office, said MPs who stood accused of sleaze allegations should "look at their consciences".
Asked whether they should stand down, he said: "If they feel that them continuing will undermine the party's efforts, and undermine the ability of the country to judge the issues rather than the sleaze campaign, then I think they have got to take that decision."
Sir Teddy Taylor, MP for Southend East, told the same programme of his "real panic", adding: "If you don't face up to this one, we are going to have the disaster, I believe, of people electing a government and not believing in the policies they support."
Sir James Spicer, the retiring MP for Dorset West, said: "This is doing us an enormous amount of damage and certainly if I were in the position where I had to put myself or the party first, I know which I would put first."
The Conservatives' problem was pinpointed by Peter Mandelson, Labour's campaign manager, who told The World This Weekend: "It's Tory MPs themselves who are saying, 'Enough is enough', and the only way to clear the campaign out of all the business of financial sleaze is for Neil Hamilton to take the appropriate action open to him, and that is to stand down. That is what I think public opinion in his own constituency will want him to do, but if he refuses to do so, then the issue will continue to dog him and the rest of his party."
Labour also said yesterday that Mr Major's decision to prorogue Parliament early, in an alleged to attempt to stifle the discussion of a cash-for-questions report from Sir Gordon Downey, Parliamentary Commissioner for Standards, had taken Mr Major's party so unawares that there had been no campaigning so far in the Tories' 80 most marginal constituencies.
Meanwhile, the sudden resignation of Sir Michael Hirst as chairman of the Conservative Party in Scotland continued to reverberate around the party yesterday, with allegations of skulduggery and dirty tricks being hurled about by friends and enemies of the former MP, who is alleged to have had a homosexual relationship.
Following the resignation of Allan Stewart as the candidate in Eastwood, Scotland's safest Tory seat, after his name had been linked with a married mother of four children, Sir Michael had made a bid to become the candidate. Sir Michael withdrew from the selection process last week, but by then, the Glasgow-based Sunday Mail newspaper had got hold of the story alleging the MP had had a homosexual relationship.
In Beckenham, Piers Merchant, the MP at the centre of allegations about a relationship with a 17-year-old girl, survived a vote of confidence. Local activists meeting in secret voted by 43-3 to endorse him as their candidate. Mr Merchant said he was "incredibly moved" by the association's support.