He is expected to pledge to keep tax rises below the rate of growth in the economy for three years, using the money saved for a range of other planned tax cuts.
The risk for Mr Davis is that if he wins the Tory leadership he will be put under relentless pressure by Labour to say which public services are to be cut.
But he is convinced that the way to defeat his rival, David Cameron, is to turn the leadership election into an argument over policy, rather than a competition about who has the more voter-friendly image.
Mr Davis received another painful reminder yesterday of how the younger contestant is proving to be a better communicator, especially with non-Tories, when Ray Mallon, Middlesbrough's Mayor, came out in support of Mr Cameron.
"Middlesbrough and the North-east is not a natural Conservative area, and I'm no Conservative supporter," Mr Mallon said. "I was elected as an independent, and that's exactly what I am.
"But I and many more people here in the North-east see something in David Cameron that we like. We see leadership. We see a guy who knows where he's going, and who has got the character and the charisma to take people with him."
Mr Davis brushed off that endorsement and insisted he could still win the contest. In an oblique swipe at Mr Cameron, who appears to be copying Mr Blair's presentational skills, Mr Davis claimed that the contest would be decided by "substance" rather than "style".
"I am firmly a low-tax Conservative," he said. "What I don't believe in is being an heir to Blair, accepting the Blair settlement. Blair won against a Tory government coming to the end of its life and would have won whatever he had done. We should not be emulating that."
He was speaking during a visit to the Base Centre in Tooting, south London, near the council estate where he grew up. The centre offers teenagers free advice on careers and personal problems. It was full of excited youngsters operating the computers, who vanished soon after Mr Davis departed. It emerged that they were there for a dance session in another part of the building, but the staff had sent them to work the computers for 20 minutes so Mr Davis would not be filmed in an empty room.
The Independent asked a group of girls how they reacted to a visit by a local boy made good. "What do you think of Mr Davis?" "Who's he?" "He's running for the leadership of the Conservative Party." No reaction. "You've heard of the Conservative Party?" "What, politics? No way! Why's there a TV camera?"
Some pro-European Tories are thinking of backing Mr Davis, despite his right-wing image. Mr Cameron has said that he will instruct Tory MEPs to leave the European People's Party, the grouping of Europe's mainstream right-of-centre parties, because it calls for more European integration. Critics say this will leave the Tories isolated in Europe. The former deputy prime minister, Lord Heseltine, told Tory MPs yesterday: "I will beg him on bended knee not to do it." Today, David Cameron is to visit Beeston, Leeds, where Mohammad Sidique Khan, the July 7 London bomber, grew up, to explain the Tories' decision to back the Government's anti-terrorism Bill.