Some senior ministers want a group of "men in grey suits" from the backbenches to urge the Prime Minister to quit rather than struggle on to his preferred leaving date in the summer.
There are no plans for a round-robin letter asking Mr Blair to depart after an attempted coup by this method failed last September. But the idea of a delegation is being discussed by Labour MPs this weekend.
The task could fall to the Parliamentary Committee, the equivalent of elected shop stewards for backbench MPs, who meet Mr Blair in private each Wednesday.
Some MPs want Gordon Brown to take over before the May elections to the Scottish Parliament, Welsh Assembly and English local authorities, fearing he may not be able to revive Labour's fortunes after more months of damaging publicity. But others say it would be better for Mr Blair to shoulder the blame for poor election results. One minister said: "We're not there yet, but we are coming to it, the way things are going. I am afraid that things are looking very bad for May."
Crucially for Mr Blair, there is no sign that the Brown camp is trying to push him out, fearing that this could damage the Chancellor. The Cabinet, which could force Mr Blair out if it asked him to go for the sake of the party, is rallying behind him. "We've only got three months to wait," said one Cabinet source. "We all have to keep our nerve."
Close allies sought to bolster Mr Blair's position. Stephen Byers, the former Cabinet minister, said: "The Prime Minister is not going to allow himself to be forced out of office by a combination of speculation and innuendo. The Tories are calling for him to go. This is the time for the Labour Party to stand united and show loyalty to the man who has led us to three general election victories."
Mr Blair believes it would damage Labour's electoral prospects if he is forced to stand down before the Metropolitan Police inquiry is completed. He has told close friends that the short-term benefit would be far outweighed by the long-term damage to Labour from him leaving under such a cloud.
The Prime Minister is said to be "frustrated" he cannot give his side of the story and to be "bemused" the investigation has already taken 11 months. He is confident he will be vindicated when all the facts are made public, but admits that may not happen until after he stands down.
Mr Blair will today appeal to his party to lift its sights above the controversy. "The fourth election will not be decided by current events," he will tell Labour's national policy forum in London. "It will be about whether we have the dynamism, energy, vision and, above all, clear, well thought-out policies for Britain's future."
He will add: "The biggest danger for us electorally is not in the end what embarrasses us, but what makes the country think that on the big challenges the country faces we only have small answers."
Yesterday Mr Blair said it would be "wrong" to quit during the police inquiry, saying that doing so to ease the pressure on the Government was "not a very democratic way to decide who the Prime Minister is".
He told BBC Radio 4's Today programme: "I'm not going to beg for my character in front of anyone. People can make up their own mind about me, according to what they think about me, but I know what type of person I am. I am not going to get into the situation where I am pleading for my integrity, not even in front of the people. I'm not going to beg for my character in front of anyone."
But some Labour MPs reacted angrily to his comment that: "You will have to put up with me for a bit longer."Jacqui Smith, Labour's chief whip, who is heading a new task force aimed at holding on to key marginal seats, warned that they would be at risk if the party "looked inwards" during the elections to choose Mr Blair's and Mr Prescott's successors. "We need to work particularly hard to show the public that it is their concerns and aspirations that we measure our aspirations by," she said.
Lord Gould, who is the Prime Minister's personal pollster, told BBC Radio 4's PM programme: "The fact that he has been questioned by police a couple of times doesn't turn an outstanding prime minister into an electoral liability. We have to take the long view; the public will take the long view and they do believe he is a remarkable prime minister."
In an interview in today's Daily Telegraph, the Conservative Party leader David Cameron further increases the pressure on Mr Blair to stand down in the "national interest".
Key dates for the PM
* Next Tuesday: Blair faces three-hour grilling at Commons Liaison Committee of select committee chairmen.
* Next Wednesday, Noon: First session of Prime Minister's Questions since disclosure that he has been interviewed by police for the second time.
12.45pm: Blair meets parliamentary committee, the "shop stewards" of Labour backbenchers, who may report unrest.
* Mid-February: Mr Blair has promised statement to Commons on Iraq policy after "Operation Sinbad".
* March: Commons vote on Trident replacement; defeat would be shattering.
* 2 May: Blair celebrates 10 years as Prime Minister (depending on whether police bring charges in honours case).
* 3 May: Heavy defeats in elections in England, Scotland and Wales could force him to announce a departure date.
* 21-22 June: EU summit hosted by Germany in Brussels that Blair says he wants to attend as PM.
* 26 July: Last day of parliament before the summer break, by which time Gordon Brown is expected to be in charge.
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