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David Maclean is understood to be ready to tell Duncan Smith that he has lost the support of the majority of the parliamentary party and should "fall on his sword".
The meeting is likely to take place on Wednesday unless the 25 MPs needed to trigger a vote of confidence have put their names forward before then.
A senior source close to the whips' office said: "We can't go on like this. It is a nightmare scenario. Iain has lost the support of the majority of MPs and he has to fall on his sword. Words like 'inevitable' and 'unsustainable' are coming from people who are strong supporters."
Maclean, who has been fiercely loyal to Duncan Smith, is understood to have decided on the move after consulting shadow cabinet members as well as other senior figures in the party.
He has also been convinced to act by the fact that loyalist MPs are now pressing for a vote of confidence after a week in which some of the party's biggest donors withdrew their backing for Duncan Smith's leadership.
Even close supporters do not believe that Duncan Smith would win a vote of confidence and are advising him to avoid the personal humiliation of a defeat by stepping down immediately. However, according to sources, the Tory leader is still refusing to take the advice, preferring instead to listen to his wife Betsy, who wants him to fight on.
Yesterday Duncan Smith's aides indicated that he would tell the party today that any move against him would amount to "political suicide" and allow the Liberal Democrats to take over as the main opposition.
Opponents of Duncan Smith claim they are only six short of the target of 25 MPs who have to submit letters to Sir Michael Spicer, chairman of the 1922 committee, calling for a confidence vote. Only one MP, Crispin Blunt, has publicly stated that he has submitted a letter; others are consulting their constituency officials this weekend.
Derek Conway, a former Tory whip, indicated that the grass-roots mood had swung against Duncan Smith, adding that the response from activists was "even more supportive [of a vote] than I expected".
Conway said: "MPs who don't relish a leadership contest came to the conclusion that it can't go on like this. That is not just those who think he is not up to the job and want a change, it is people who will still vote for him in a leadership contest."
John Greenway, MP for Ryedale, also spoke out for the first time, saying that a confidence vote "would seem to me to be the only way of resolving the situation".
He added: "What I would hope is that Iain would submit himself to that [vote] so that members of the party who have never been disloyal don't have to take the situation into their own hands."
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