Brown, whose Labour Party is languishing in third place in opinion polls, was forced to make a humiliating public apology to Gillian Duffy, 66, when his "bigot" remark was picked up by a microphone on Wednesday.
The prime minister said on Thursday that he was determined to focus on economic matters and will hope that a good performance in the debate can help turn his fortunes around.
Alan Johnson, a senior Labour minister, said that Brown would be "pulling out all the stops" in the third and final televised debate.
The issue of Britain's spiralling public debt and how best to bring it under control has been a key issue in the election campaign, which comes as the UK shows signs of a feeble recovery from recession.
Cameron's Conservative party has argued for deep cuts to public spending to reduce the deficit, but Labour says that the approach could plunge the country back into recession, and advocates a less pronounced spending slowdown.
The US-style leaders' debates have proven hugely influential in the campaign so far.
The Liberal Democrats, traditionally Britain's third party, have surged in opinion polls following strong performances from Clegg in the first two debates.
All three leaders will be anxious not to slip-up in the debate, but face a difficult task as they attempt to discuss the extent of the spending cuts without scaring off voters already feeling financially bruised by the recession.
Experts say that whoever ends up forming the next government will need to implement serious austerity measures that will be unpopular with voters.
David Hale, a US economist, said that Mervyn King, the governor of the Bank of England, had told him the election would prove a poisoned chalice for the eventual winners.
"Whoever wins this election will be out of power for a whole generation because of how tough the fiscal austerity will have to be," he said the governor had told him.
With just a week left in the race for Downing Street, polls suggest the country is headed for a hung parliament, where no clear winner emerges.