Mr Cameron was challenged to say what he would do about the 10p rate
David Cameron has urged voters in Crewe and Nantwich to back the Tories in a bid to get Gordon Brown to take action over the scrapping of the 10p tax rate.
He said a Tory win in the Labour-held seat would send a clear "message" to the PM that he needs to do more to help those hit by the controversial measure.
His party will give its "best shot" to overturn the late Gwyneth Dunwoody's 7,078 majority, he said.
Justice Secretary Jack Straw said the 10p tax issue was "being dealt with".
The by-election was triggered by the death of 77-year-old Labour veteran Mrs Dunwoody last month.
As Mr Cameron toured Crewe and met Tory candidate Edward Timpson, he was challenged by one voter to say if he would restore the 10p tax rate.
The man told him that "a gallon of petrol is an hour's work", and pressed Mr Cameron to say if he would "give that 10% back".
Conservative leader David Cameron on 'turning the economy round'
Mr Cameron said he "couldn't make that promise now", but claimed voting Conservative could get that message to Mr Brown.
The abolition of the lowest rate of income tax came into effect last month, alongside a reduction in the basic rate of income tax from 22p to 20p and increases in child benefit and tax credits.
The government has said it will outline a compensation package for pensioners aged 60 to 64 and low earners before this autumn's pre-Budget report.
Speaking at his monthly news conference, Mr Cameron said winning the Crewe & Nantwich seat was the Tories' "top campaigning priority".
He said Thursday's local elections, which saw Labour pushed into third place behind the Lib Dems, had "banished forever" the idea the Tories "can't win seats in the north of England".
"We have got 15 days to overturn Labour's majority of over 7,000," he said.
"Obviously it's going to be a tall order, but we're going to give it our best shot. We have a strong local candidate and a real focus from the entire organisation.
"Our message will focus in particular on the 10p tax rate and how Gordon Brown is hurting the people of Crewe with tax increases just at the moment their cost of living is going up.
"People in Crewe know that the more of them who vote Conservative on 22 May, the clearer the message will be to Gordon Brown to do more to help those who have suffered from the tax con Budget."
Tory candidate Mr Timpson will face Labour contender Tamsin Dunwoody - the daughter of veteran MP Mrs Dunwoody - and the Lib Dem candidate, former banker Elizabeth Shenton.
Mr Cameron said he was ready for a general election, should it come sooner than 2010, saying they were on a "permanent" election footing.
He said a Tory government's top priority would be the NHS, reform of schools, welfare and making families stronger.
He urged Mr Brown to reopen the Budget, which he described as "a disaster".
Darling rebel talks
However, Lib Dem Treasury spokesman Vince Cable accused Mr Cameron of crying "crocodile tears", claiming "the only tax cuts he has proposed are for millionaires".
Meanwhile, Chancellor Alistair Darling was set to hold talks with former welfare minister Frank Field and ex-whip Greg Pope to discuss the government's proposals to provide partial compensation for those worst hit by the abolition of the 10p rate.
Mr Straw, who met Labour supporters at Crewe's Coppenhall Working Men's Club, said measures to off-set the loss of income expected by some people would be announced as soon as possible.
"There is no question that people are worried over economic issues. Fuel prices and energy prices for their home are rising and there is anxiety about house prices too," he said.
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