Mr Cameron said his party's savings pledges were 'do-able'
The Tories have detailed how public spending could be cut by £12bn to fund their pledge on National Insurance.
Tory leader David Cameron said cuts to IT projects, office costs, contracts and recruitment were "do-able".
Labour has dismissed the savings, some of which the Tories would use to curb a planned NI rise, as a "fantasy".
Labour and the Liberal Democrats say the savings would mean public sector job cuts while the Tories say an NI rise is a "jobs killer" for firms.
In Friday's other election developments:
On the fourth day of the campaign tax and spending continued to dominate the clashes between the parties.
Labour wants to raise NI by 1% for people on more than £20,000 from April 2011 to protect spending on health, schools and policing.
The Tories say that would "kill the recovery" and is a "tax on jobs" - their plans to block the rise are backed by 81 business leaders.
They would fund that policy by making savings elsewhere - but Labour say it is a "fantasy" to suggest they could save £12bn of public spending in the coming year.
But Conservative adviser Sir Peter Gershon, who used to be the government's efficiency adviser, told the Financial Times that £9.5bn could be saved by cutting IT costs, renegotiating contracts, curbing consultants.
He said "perhaps £1bn to £2bn" could be saved by curbing recruitment - prompting estimates that 20,000 - 40,000 public sector jobs could go.
Conservative leader Mr Cameron told BBC Radio 4's Today programme: "It is do-able, it is deliverable, I don't think it's particularly challenging to ask government to save £1 out of every £100 it spends.
He would not confirm how many fewer public sector jobs there would be under a Tory government, but he said: "It's not talking about people losing their jobs, it's talking about not filling vacancies as they arise."
'Calmly and reasonably'
He said a Tory government would make changes "along the lines of" what Sir Peter had suggested, in consultation with the Treasury.
"The exact balance between things like procurement, recruitment and IT should be decided calmly and reasonably with the Treasury if we are elected on 6 May."
He said not replacing "back office" and management jobs meant more money could be saved for the front line and denied it was a "plan to fire people".
SIR PETER GERSHON
He may advise the Tories, but Sir Peter used to be a Labour adviser on efficiency savings.
In 2003, he was appointed to lead the government's own efficiency review.
He returned to the private sector and was knighted in 2004.
The Tate and Lyle chairman used to be MD of Marconi and head of the Office of Government Commerce.
Gordon Brown has dismissed the Conservatives' plans to save £12bn as built on a "myth" and Chancellor Alistair Darling said some of the savings had already been made by the government.
Mr Darling added: "It is now clear from [David Cameron's] interview on Today - and he was unable to deny this - that additional heavy cuts will have to be made in public sector spending and jobs from this year onwards and that tens of thousands of jobs will be lost, not just in the public sector but in the private sector as well, where they depend on government contracts."
But Treasury minister Stephen Timms told the BBC the government's own plans to save £15bn would involve redundancies.
"There will be some job losses, without a doubt," he told the Daily Politics.
Asked if the public sector would be smaller than today in terms of jobs by 2014, he said: "My sense is, it will be smaller. How much smaller will depend on the outcome of the spending review later in the year."
Lib Dem Treasury spokesman Vince Cable said it appeared Sir Peter Gershon was "looking to immediately slash employment throughout the public sector".
But his party leader Nick Clegg told GMTV he would make some job cuts.
He highlighted the NHS, questioning the role of strategic health authorities.
"These are pen pushers in the NHS, get rid of them so we can use the money... to protect the A&E departments, the maternity units, the GP services."
He said 5,000 more "bureaucrats" were employed in the NHS last year, while the number of nurses had only increased by 2%.
On Friday the Tories are outlining plans to curb excessive public sector pay and to strip some payments from those repeatedly caught committing benefit fraud.
The Lib Dems have pledged to stop banks charging customers unfairly for going over their limit or bouncing a cheque.
And Labour are highlighting the role of the DNA database - the Tories oppose keeping the DNA of people arrested for minor offences but not charged.