David Cameron is building support among Tory MPs as the three remaining leadership contenders battle to woo voters ahead of Thursday's crunch vote.
Mr Cameron: Support is growing
Mr Cameron has picked up 11 more backers since Ken Clarke was knocked out in the first round on Monday.
The BBC's Nick Robinson says some Tory bosses have been told to prepare for a new leader by Friday if Mr Cameron wins the poll overwhelmingly.
Liam Fox says the plan is unthinkable. Davis Davis says he is fighting to win.
Ken Clarke was eliminated in Tuesday's first round with 38 votes. Mr Davis came first with 62 votes, Mr Cameron got 56 and Dr Fox 42.
Mr Cameron's hopes of winning the contest received another boost on Thursday with a YouGov poll for the Daily Telegraph suggesting that 59% of ordinary party members - who will decide the outcome - wanted him to take the helm.
This put him well ahead of Mr Fox on 18% and Mr Davis on 15%.
YouGov interviewed 665 Conservative Party members across the UK online on Tuesday night.
Thursday's vote should select the two who go to a ballot of party members.
But BBC Political Editor Nick Robinson said some Tory party officials and some Davis supporters believe he could stand aside in the event that Mr Cameron wins the poll convincingly.
"They recall how Mr Davis stood aside to Michael Howard to become Tory leader unopposed," said Robinson.
But the Davis team say the election rules state specifically that neither of the last two remaining candidates can pull out of the contest without the agreement of the chairman of the backbench 1922 committee and the Conservative Party Board.
A spokesman for Mr Davis added: "David is fighting for every vote, is confident he will go through to the next round and intends to take the contest to the party membership and win."
Dr Fox said: "After all the consultations of recent months it would be unthinkable if the members were denied their say in the leadership election.
"Those who favour such an approach demonstrate astonishing arrogance."
NEW CAMERON SUPPORTERS:
Sir Malcolm Rifkind
Sir George Young
David Heathcoat Amory
In an eleventh hour pitch for votes, Mr Davis told the BBC that as Conservative leader he would push for good public services, low taxes and opportunity for youngsters.
"That is what I am talking about delivering when I become the next Conservative prime minister," he added.
Mr Cameron told the BBC his priorities as Tory leader would be to make the economy more competitive, to strengthen families and communities and improve the quality of life for everybody.
"People are switched off politics and I want to try and switch them back on by being a voice for optimism, for change and for hope," he said.
NEW FOX SUPPORTERS:
Stewart Jackson, who switched support from Mr Davis to Mr Cameron, said he had a "fresh approach, people are relating very well to him, he's uniting the party - he's an election winner".
Sir Malcolm Rifkind, an ex-Clarke supporter, now Cameron convert, told BBC Radio 4's Today: "I didn't know David Cameron very well until recently. What I've seen, the more I've met him, the more I've heard him, the more impressed I've been."
Former Clarke-supporter Quentin Davies said he was now voting for Mr Davis, because he would make a "credible prime minister".
Ex-Clarke backer Ann Widdecombe said she would be backing Dr Fox "because I want to see him in the last two", although she reserved her position when the fight goes to party members.
Dr Fox told the BBC as Tory leader he would want to see a Britain "where hard working people get to keep more of their own money, where we encourage enterprise and prosperity."
The shadow foreign secretary's aides say John Redwood, John Whittingdale, Nigel Waterson and Laurence Robertson are also now publicly backing Dr Fox.
Former minister David Heathcoat Amory has admitted he voted tactically for Dr Fox to knock out Mr Clarke but will now back Mr Cameron.
The final result of the party members' ballot is expected on 6 December.
Michael Howard, who has formally resigned as leader, will carry on in a caretaker role until then.