"It's a heavy responsibility," said Mr Blair at the carefully stage-managed by-election meeting with eight Tory deserters. "People don't expect miracles, but they do expect us to make a start."
Pauline Williams, a past Tory voter, told the Labour leader: "We have given them long enough ... You have a responsibility. We are hoping you are going to answer everybody's prayers for us."
Another Tory deserter, Wilf Round, said: "You arrived at the right time."
The Labour leader regarded the power of the "Blair factor'' as a mixed blessing, which he sought to play down. It was "quite wrong" to think his personality was the main reason for the Tories switching their votes to Labour, Mr Blair said after the meeting in a country hotel.
"They are very interested not in every specific detail of policy but in the character of the new Labour Party...You are wrong in thinking this was just disillusion or liking of the new Labour Party. It is much deeper than it," he said.
His aides, nervous of voter apathy, urged caution over an opinion poll giving Labour a 55-point lead over the Tories with Labour on 71 per cent, Tories 16 per cent, and the Liberal Democrats 11.
Paddy Ashdown, the Liberal Democrat leader, threw cold water on Labour hopes that Dudley West will mark the turning point to a Labour general election victory. It was a snapshot, he said, but it will be a serious blow for John Major, if the Liberal Democrats can push the Tories into third place in the seat, which they have held since 1979.
The informal meeting with Mr Blair was designed to give wavering Tory voters the spur in the last 48 hours before tomorrow's by-election to make the switch to Labour, rather than to lodge a protest vote with the Liberal Democrats or stay at home. Mr Blair repeatedly stressed the word "new" when mentioning the Labour Party. The only point of discomfort with his new-found friends from the Tory party came when they got on to law and order. Fearing they might start demanding the return of the death penalty under Labour, Mr Blair moved them on to safer ground.
He asked the eight deserters whether they would vote Labour at the general election. Michael Ellwood, 45, an electricity board worker, from Pensett, said: "It's not a protest vote. I have done that in the past. I want a change. I want them out."
Joy Round, from a staunch Tory family, said the Tories had been in power for too long and had become "arrogant - they are out of touch with the ordinary person".
Mr Ellwood said he was disillusioned over broken promises on tax cuts. "We are getting back to the Victorian age. We are back to the tugging of forelocks. If you don't like it, there is the door..."
But Mr Ellwood, accompanied by his wife, Tracey, 33, and their daughter, Natalie, two, told Mr Blair: "We don't want to get back to the days of Red Robbo - everyone out brothers, out."
This also was dangerous ground, which Mr Blair quickly moved off. He said: "You don't want to go back, but you do want some new sense of fairness in society..."
The conversation kept coming round to the subject of his own leadership. Mrs Round said: "I think Tony Blair is a strong character. He is a young leader. That is just what we need. I think he has got brains."
Mr Blair said: "You finally made a politician blush."