Mr Brown will return from the US to backbench anger
Five more ministerial aides have joined protests at the abolition of the 10p tax rate.
The five junior government members have called on Gordon Brown to help 5.3 million low-paid workers who have lost out as a result of the changes.
On Thursday Mr Brown had to persuade ministerial aide Angela Smith not to quit over the issue.
The Treasury has denied reports the chancellor is preparing a climbdown over the abolition of the 10p tax band.
The Daily Telegraph reported Treasury officials were working on plans to compensate low-earning workers without children who are losing money, following the scrapping of the 10p rate.
But a Treasury spokesman told the BBC there was no thought of "an imminent change to the policy".
He said the chancellor was aware of people's concerns and in future "would take them into account".
Mr Brown is said to be furious the tax row overshadowed his trip to the US.
He is understood to believe it has been exaggerated by the media and has urged Labour MPs to look at the government's overall tax changes, which he says have helped low-paid families.
David Anderson, Jeff Ennis, Celia Barlow and David Kidney are parliamentary private secretaries (PPS) who have called for more help for those affected by the reforms on the 10p band.
Stephen Pound, PPS to Employment Minister Stephen Timms, has also expressed unease at the current situation.
He told Channel 4 News the issue had become "corrosive" and there was a "groundswell" of opinion about it.
No-one has threatened to resign over the issue.
Mr Ennis, aide to Cabinet Office minister Ed Miliband, told the Evening Standard: "The die is cast on the 10p rate but we have to listen to what people tell us and in future redress the balance."
Mr Anderson, aide to higher education minister Bill Rammell, told the Standard: "We should not be making poor people poorer and at the same time giving people extra money through inheritance tax."
But he said he would not threaten to resign over the issue.
Celia Barlow, aide to science minister Ian Pearson, said in a statement she was not planning to resign her position.
But she added: "I have, however, written to the prime minister and the Chancellor to express my concern over the effects that the abolition of the 10p tax rate will have on some of my constituents.
"I have also forwarded them copies of constituents' letters and e-mails that I have received detailing the effects of the abolition."
Mr Kidney, aide to junior transport minister Rosie Winterton, has also written to the prime minister about the abolition of the lowest tax band.
He said it was his job as a constituency MP to raise matters of concern with ministers.
They have joined a growing number of Labour backbenchers in expressing their anger at the changes, which came into effect this month.
Sheffield Attercliffe MP Clive Betts has written to Mr Brown urging him to reverse the changes - something consistently ruled out by Mr Brown.
Mr Betts told BBC News 24 people on low incomes without children had been left paying more tax.
Ms Smith said she had 'concerns' but would not resign
"That's something that we really feel unhappy about and we'd like the government to recognise that they have got that element wrong and take steps to put it right as quickly as possible."
MPs will debate the second reading of the Finance Bill on Monday.
But they will not get a chance to vote on the 10p tax issue until a week later, when ex-minister Frank Field plans to table an amendment calling for compensation for those affected, at the bill's committee stage.
Mr Field said he hoped the government would make the changes itself, rather than being forced to do so.
"We have never had a measure where we are being asked to vote for a package which makes five million of the poorest people worse off," he told BBC Radio 4's Today programme.
On Thursday, Mr Brown called Angela Smith from the White House, after reports suggested she was considering resigning from the government.
Ms Smith, PPS to Chief Secretary to the Treasury Yvette Cooper, said in a statement she had had "concerns" but had been reassured they were understood and "the government remains committed to its anti-poverty agenda".
The row has been seized by the opposition as a sign that Mr Brown is losing control of his own party.
Conservative leader David Cameron told Sky News: "It's rather extraordinary, he seems to have very little authority now, he's being held to ransom by members of his own front bench, threatening to resign and then he's having to break off from trips to the US to dissuade them."
And Liberal Democrat leader Nick Clegg said: "Gordon Brown's government is starting to unravel before our eyes as Labour MPs see the full extent of the prime minister's betrayal of the most needy in our society."
Mr Brown decided, while still chancellor, to abolish the lowest, 10p rate of income tax and to reduce the basic rate from 22% to 20%.
He has defended the move saying: "I am satisfied that once people understand the scale of the good things that we have been able to do in reforming the tax system, that we are tackling poverty by increasing tax credits for the poorest, then whatever questions people have about these changes can be answered."