Wednesday's PBR announced belt-tightening measures including a public sector pay cap and a rise in National Insurance, but both of these come in from 2011.
BBC Political Editor Nick Robinson said the disagreement between the Treasury and No 10 was not about the speed at which the budget deficit should be reduced, or Alistair Darling "siding with the Conservatives" in arguing for the deficit to be cut sooner and faster.
It was, instead, about how to ensure that the government appeared to have a credible and convincing plan to achieve its stated objective of cutting the deficit in four years.
Mr Robinson said: "The pre-Budget report actually increased the spending plans the chancellor had previously set out in his Budget, despite the fact that Britain faces the worst peacetime deficit in its history.
"One reason for this is an aggressive public and private campaign by [Schools Secretary] Ed Balls for a real-terms increase in school spending.
"He wanted to create a political 'dividing line' with the Conservatives, who have promised to increase spending on health in real terms but have made no similar pledge about education.
"The prime minister sided with the man who was his Treasury adviser during his long period as chancellor. Although Mr Balls didn't get as much as he wanted, he did get agreement for a 0.7% increase in school spending."
The Treasury has denied a report in the Guardian newspaper suggesting that No 10 blocked a plan to impose a VAT rise above 17.5%, saying that was never an option.
The Conservatives claim the Treasury privately backed their calls for a "more credible plan" to reduce the deficit to gain credibility with the markets, amid fears of a run on the pound leading to increases in interest rates.
Shadow chief secretary to the Treasury Philip Hammond told the BBC News channel: "The chancellor had the opportunity on Wednesday to set out clear future departmental spending plans showing where the reductions in public spending would come, so that people could see that he was really serious about this."
But he said Mr Darling "ducked the issue and went along with the prime minister's proposals simply to try and create some political dividing lines rather than doing things the British economy needed done in order to support the recovery".
Thursday saw one of the biggest sell-offs of gilts - the bonds the government sells to raise money - as investors fretted about the long-term outlook for the UK's public finances.
It came as leading economists warned that not all the cuts needed to reduce the deficit had been outlined by the chancellor.
The Institute for Fiscal Studies (IFS) says public spending is facing a £36bn squeeze from 2011 - with £15bn of the cuts needed yet to be identified.
With health and education protected, the axe could fall on defence, housing, transport and higher education.
The think tank predicted "severe cuts" of the kind not seen in the UK since the late 1970s.
But Justice Secretary Jack Straw said the IFS had not taken into account savings already made by the government due to lower than expected increases in unemployment.
Lib Dem Treasury spokesman Vince Cable, who argues that no areas of public spending should be off limits when it comes to cuts, called for a "proper debate" on where the axe should fall.
"Because they are not discussing priorities openly a great deal of damage is being done," he told BBC News.
Meanwhile, an opinion poll for the BBC suggests Mr Brown and Mr Darling are less trusted to steer Britain's economy through the economic downturn than Conservative leader David Cameron and shadow chancellor George Osborne.
The poll, for BBC Two's Daily Politics programme, was carried out by ComRes after the PBR.
A third (33%) of those questioned said they trusted Mr Cameron and Mr Osborne most on the economy.
That compared with 26% saying they trusted Labour's Mr Brown and Mr Darling - a lead of seven percentage points for the Conservatives.
In a similar poll conducted in April, Mr Brown and Mr Darling had a lead of three points.
The Liberal Democrats recorded their highest rating yet to this poll question - with 16% saying they trusted party leader Nick Clegg and Mr Cable most. This compared with the April figure of 10%.
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