He said there was "widespread scepticism" among the public and retailers about the proposal's "merits".
"There are running away from the argument because they are losing the argument," he told MPs.
Unlike the Budget, the pre-Budget report (PBR) is not usually followed by a debate but the Tories argue this one was a Budget in all but name.
The debate will start an hour after the weekly Prime Minister's Questions, likely to be dominated by economic arguments.
Among them will be the proposal to increase VAT to 18.5% from 2011 - which was apparently mistakenly included in documents published alongside the PBR online.
Mr Cameron said the government had promised to show how they would pay for its plans but the document showed they were planning a VAT increase.
He told the BBC: "That's why the budget doesn't add up, that's why there's such a big black hole, that's why everyone is saying this budget isn't convincing and it isn't. There's a secret tax bombshell coming down the road at every family in the country."
The Treasury says the proposal "was considered and rejected" and the chancellor always considered "a range of policy options, most of which are rejected".
A spokesman said the final decisions were clearly set out in Monday's PBR.
Earlier Mr Osborne has said the country was facing "huge risks" and a "trillion-pound" public debt from measures outlined in the PBR.
Lib Dem leader Nick Clegg has urged ministers to get "really tough" with banks to force them to increase business and personal lending or to "bypass" them by injecting money into the economy through other routes such as local authorities or the Post Office.
It comes as Bank of England Governor Mervyn King told MPs it was essential banks started lending again at normal rates and "in the last resort", the government may need to "intervene directly to ensure the flow of lending continues".
In his report on Monday, the chancellor unveiled plans for record borrowing and the VAT cut.
To pay for that in future years Mr Darling said that from 2011 National Insurance would rise by 0.5% and there would be a new 45% tax rate for earnings above £150,000. There would also be a sharp slowdown in public spending growth.
Darling warns banks on lending
Mr Darling is gambling that an increase in borrowing will diminish the downturn.
He denied that the New Labour project - which ruled out raising income tax rates - was dead.
Mr Darling told the BBC's political editor Nick Robinson that people earning more than £150,000 would shoulder the "lion's share" of the tax increases from 2011 onwards.
He also defended the decision to sharply raise borrowing levels to help the economy through the recession saying it would make the "pain shorter and make sure we get through this quicker than would otherwise be the case".
Liberal Democrat Treasury spokesman Vince Cable said the pre-Budget report measures did not go far enough and that he doubted that the VAT cut - which will cost £12.5bn - would be sufficient to give the economy a boost.
He said the government "had to do something", but added: "Our criticism is about the way they did it.
"We think the tax cuts should have been concentrated on low-paid workers, people on low, middle incomes, cutting their income tax on a permanent basis and financing it from the top end of the scale."
The Lib Dems have tabled a motion calling for the VAT cut to be dropped although there is little chance of it going to a vote.
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