Mr Brown is facing calls from some of his own MPs to explain the compensation package better to voters, with one, Graham Stringer, telling BBC News that voters had reacted with "disbelief and hostility" to the axing of the 10p rate.
He is also trying to avoid a possible Commons defeat over plans to extend the length of time terror suspects can be held without charge to 42 days.
Foreign Secretary David Miliband rejected press reports that Mr Brown was preparing to do a U-turn on that issue too.
And asked if Mr Brown would have to step down if Labour suffered heavy losses at Thursday's local elections, Mr Miliband replied "No, definitely not."
He told BBC One's Andrew Marr show the party had to "fight back" against the "mid-term blues" and could not afford to "roll over and say 'we have had enough'".
He said: "We always knew this was going to be a very tough year because it's the mid-term of third term and we have got a world economic situation that is very, very difficult indeed.
"And I think this is a test of character really as well as a test of policy.
"We know what's fatal - if we fail to defend the leader, if we lose sight of our core convictions, or we don't follow through on what we have started."
He said the government had to "keep very close to the concerns of voters and that's why the decision this week about the 10p rate was right".
Justice Secretary Jack Straw conceded that the government was facing "difficulties" at present but that this had happened before and Labour had been re-elected.
Lord Levy said he was 'disappointed' by Labour's recent slide
Labour deputy leader Harriet Harman told Sky News it was "rubbish" to suggest Labour MPs wanted to get rid of Mr Brown - and European trade commissioner Peter Mandelson, a close ally of Mr Blair, warned Labour to "pull itself together and refocus".
The former cabinet minister dismissed Lord Levy's claim that Mr Blair thought Mr Brown could not win the next election - saying he had been 100% loyal.
In his memoirs, which are being serialised in The Mail on Sunday, Lord Levy writes that Mr Blair "told me on several occasions he was convinced Gordon 'could never beat Cameron'".
The newspaper quotes the peer as saying Mr Blair claimed he was convinced he could win a fourth term if he stayed on at Number 10.
"But Gordon? 'He can't defeat Cameron,' Tony told me," Lord Levy writes.
"Blair believed Cameron had major strengths - political timing, a winning personality and a natural ability to communicate to Middle England that Gordon would be unable ever to match."
Lord Levy, who was at the centre of cash-for-honours allegations, also attacked the "lack of strong leadership" in the Labour Party.
The peer denied any wrongdoing over cash-for-honours allegations and no charges were brought against him or anyone else.
Tory poll lead
A spokesman for Mr Blair insisted the ex-PM was fully behind Mr Brown and believed he could win the next general election.
"Tony Blair said when he stood down that he would be 100% loyal to Gordon Brown and that continues to be the case.
"He doesn't agree with the views attributed to him by Lord Levy and fully believes Labour with Gordon Brown's leadership can win the next election."
Tory leader David Cameron has meanwhile told the Andrew Marr show he will not be distracted by a new opinion poll suggesting he will become prime minister with a strong majority at the next general election.
The ICM survey of marginal seats for the News of the World suggests 131 Labour MPs would be ejected from the Commons in favour of their Conservative challengers.
The findings point to a 9% swing from Labour to the Tories, giving Mr Cameron a 64-seat majority.
But another poll by ICM, for The Sunday Telegraph, puts the Tories on 39% nationally, 10 points ahead of Labour on 29% and the Lib Dems on 20%.
Lib Dem deputy leader Vince Cable said his party should be doing better, given the problems afflicting the government.
"We are not doing badly but we could do a lot better," said the Lib Dem Treasury spokesman.
"I think it's a question of us putting in more work, being credible on the issues that really matter to people."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.