Tory leader David Cameron is facing new calls to commit the Conservative Party to a policy of tax cuts.
The Thatcherite No Turning Back Group pushes such a move in a pamphlet unveiled at the party's conference.
The call by the group, chaired by the former minister John Redwood, focuses on longer term aspirations rather than setting out specific policies.
Shadow chancellor George Osborne said he could not pledge tax cuts - adding it was "conceivable" taxes could rise.
Mr Osborne said his top priority had to be keeping interest rates and inflation low.
Mr Redwood denied he was at odds with his leader and said Mr Cameron would accept the longer term case he was proposing.
He said he backed Mr Cameron's call for any proceeds of economic growth to be shared between spending on public services and tax cuts.
The former minister said it was likely there would be some economic growth under a Conservative government if current tax levels remained the same.
"But I am also going to argue today that if you are able to reduce tax rates you get faster economic growth," he said.
Mr Redwood pointed to the Republic of Ireland which had seen growth "three times" more than the UK over the same period. This, he said, was because of lower tax levels.
Lord Blackwell, who ran the Downing Street policy unit in John Major's government, said he thought taxes could be cut by between £20bn and £30bn over the next Parliament.
He said ensuring that public spending rose 1% slower than the growth of the economy would leave room for those tax cuts - and still see spending on public services increase by £40bn.
Edward Leigh, Conservative chairman of the Commons public accounts committee, claimed that at least 100 Tory MPs wanted plans for tax cuts set out immediately.
He warned: "If the Conservative Party does not promise tax cuts then it's nothing."
Mr Leigh said the Conservatives would be "torn apart" by Chancellor Gordon Brown, the most likely next Labour leader, if they were "all spin".
'Not pushed around'
But Mr Cameron said Mr Leigh was wrong and had "misread history" as Margaret Thatcher had promised stability, not tax cuts.
Answering questions from BBC viewers, listeners and website users, Mr Cameron said people wanted to know the Conservatives would put economic stability first and ensure mortgage rates were kept low.
"We can't make promises we can't keep," he said, vowing not to make "reckless" promises or be "pushed around".
Earlier, Mr Osborne said the Tories wanted to move towards lower taxation but it was unlikely he would be able to make up-front promises of tax cuts ahead of the next election.
Asked if taxes could rise under a Tory government, he replied: "It is conceivable, not least because taxes went up under Margaret Thatcher's first government but that's certainly not our intention."
Mr Osborne said he wanted to reduce the share of national income used for public spending - but refused to put a figure on what he would like the share to be.
The tax debate is likely to be intensified when the party's tax reform commission reports back later this month.
That group, headed by former minister Lord Forsyth, is also expected to call for tax cuts of up to £19.5bn, including a cut in the basic rate of tax.
Meanwhile the UK Independence Party is planning to unveil its own plans for a 33p flat-tax rate on Tuesday in Bournemouth.
UKIP also backs tax free allowances of £9,000, inheritance tax scrapped and Capital Gains reduced to 33%.