Mr Brown has not been to campaign in Crewe and Nantwich
David Cameron has accused Gordon Brown of hiding in "his bunker" - instead of going out to Crewe and Nantwich to explain axing the 10p tax band.
Mr Brown told MPs it was a prime ministerial convention not to campaign at by-elections and he had given £2.7bn to help those hit by tax changes.
Mr Cameron taunted him by saying his predecessor as PM, Tony Blair, "led from the front" at by-elections.
It came as all parties made a final push for votes in Thursday's poll.
Labour deputy Harriet Harman, shadow home secretary David Davis and Lib Dem leader Nick Clegg are all in the area to support their respective candidates.
The by-election was sparked by the death of Labour MP Gwyneth Dunwoody, who had held the seat since 1983.
At prime minister's questions in the Commons, Mr Cameron accused Mr Brown of planning another "tax con" by making tax cuts introduced after the 10p U-turn for one year only.
The Tory leader, who has made several visits to Crewe during the by-election campaign, said it was a "huge issue" for voters and asked if the £2.7bn compensation package would be continued next year.
Mr Brown replied: "We've already said that we want to continue to help those affected by the 10p rate and the chancellor will announce that in the Pre-Budget Report."
But Mr Cameron hit back: "This is a one-off, one year only change. The government giving some people some money this September and taking it all back again in April.
"It is just one tax con followed by another."
Mr Brown rejected this, saying the government was giving a tax cut to those who needed it - people on low and middle incomes.
To which Mr Cameron asked why Mr Brown had not had "the courage to explain these points to people on the streets in these towns".
Mr Brown said it was convention that prime ministers did not campaign in by-elections, but Mr Cameron hit back that Mr Blair had done so.
"Instead of leading from the front, haven't you put yourself into your bunker?" he said.
Mr Brown said Mr Cameron wanted people to believe his party helped the poor, yet it had opposed tax credits, the minimum wage and maternity leave.
"You can get by without substance for some of the time, but you will never get by without substance all of the time."
Ladbrokes have stopped taking bets on the outcome of the by-election because the Conservatives have become "unbackable" at 16/1 on.
The Lib Dems - who specialise in snatching surprise by-election victories - have been trailing in the opinion polls in Crewe and Nantwich.
But deputy leader Vince Cable insisted on Tuesday's Newsnight the Lib Dems were taking their chances of success very seriously.
"What's very clear is there is a lot of support draining away from the Labour Party - an enormous amount," he said.
Labour has come under fire for accusing the Conservative candidate Edward Timpson - a barrister whose family founded the Timpson shoe repair business - of being a "toff" while their campaign promotes Ms Dunwoody, daughter of the late Gwyneth Dunwoody, as "one of us".
But Labour's chief whip Geoff Hoon told Newsnight the party's campaign was about "choosing the best person to best represent the people of Crewe and Nantwich" and he said Ms Dunwoody was "an excellent candidate".
At the 2005 general election, Gwyneth Dunwoody won the seat for Labour with a 7,078 majority.
But a survey of 1,001 adults in Crewe and Nantwich by ComRes for the Independent, published on Tuesday, gave the Conservatives a 13 point lead on 48%, compared with Labour's 35% and the Lib Dems on 12%.
Here is a list of the 10 candidates for the Crewe and Nantwich by-election on Thursday 22 May:
The Flying Brick - The Official Monster Raving Loony Party
Tamsin Dunwoody - Labour
Gemma Garrett - Independent
Mike Nattrass - UK Independence Party
David Roberts - English Democrats
Elizabeth Shenton - Liberal Democrats
Robert Smith - Green Party
Paul Thorogood - Cut Tax on Petrol and Diesel
Edward Timpson - Conservatives
Mark Walklate - Independent