Mr Brown says the Tories have revealed their true priorities
Gordon Brown has again accused the Conservatives of planning "savage" public spending cuts after the next general election.
The prime minister told the Sunday Mirror the Tories had "let the cat out of the bag" about planned 10% cuts.
But for the Tories, Ken Clarke said it was a "childlike deception" to pretend the PM would protect public spending in the face of a "serious debt problem".
Independent experts believe cuts will happen whoever wins the next election.
Speaking to the BBC this week, Tory health spokesman Andrew Lansley appeared to suggest that, in order to protect spending on the NHS and schools, a future Conservative government would cut expenditure in other areas by a total of 10% between 2011 and 2015.
The Conservatives said he had been working from Labour's own figures from the last Budget, which showed departmental spending - rather than the overall headline public spending figure - will be cut by 7% in real terms from next year.
But in his article, Mr Brown accused the Tories of devising a "cuts plan that is wide, deep and immediate in order to fund a £200,000 tax cut for the 3,000 richest families" - a reference to a Conservative pledge to scrap inheritance tax on properties worth less than £1m.
Branding Mr Cameron "Mr 10%", he said the Tory leader "would actually make the recession worse, by slowing public spending at exactly the time we need it most".
He said a 10% spending cut would mean "44,000 fewer teachers, 15,000 fewer police, 10,000 fewer soldiers and, each year, 32,000 fewer university places".
He added: "Those aren't just numbers on the page, but real jobs hanging in the balance."
'Grown up debate'
Asked about the row, shadow business secretary Ken Clarke told the BBC One's Politics Show: "Gordon Brown's been pretending that we are the party of cuts and he's the party of investment, despite the public figures saying real spending's going down even on Labour's announced plans.
"Now if the prime minister was stupid, I would forgive him. But he's not stupid.
"He's a highly intelligent man and it's a kind of child-like deception that he is somehow continuing to maintain public spending if he's allowed to keep in office.
"Were he to do that he'd ruin the country because the public finances are already a terrible mess."
He said the public knew there would be "tough and difficult decisions" and it was up to politicians to have a "grown up debate" about it.
Vince Cable, the Treasury spokesman for the Liberal Democrats, told the BBC it was a "very artificial argument".
"We are talking about these growth figures which are based on a baseline that the government itself has established, which does involve real cuts in services and involves savage cuts in public investment.
"I think the trap the Tories have fallen into is that they are promising immediate cuts when we are still in the middle of a recession, rather than talking about the next 10 years when we are going to have to make some very, very tough choices about spending priorities."
At this stage, the two main parties have not spelt out their detailed spending plans beyond 2011 but the debate will intensify in the run-up to the election.
In its analysis of the Budget in April, the respected Institute of Financial Studies said the country faced "two parliaments of pain".
It said there was £90bn "black hole" in the public finances and it would cost £2,480 in higher taxes or spending cuts per family to bring the budget back into balance.
Labour disputed this figure and said the IFS had not understood the full picture.