Tony Blair is likely to stay as prime minister longer than some had expected, Education Secretary Alan Johnson said.
Mr Blair's record was praised by Bill Clinton
Buoyed by Mr Blair's final conference speech as leader, his supporters want him to stay until next summer.
Mr Blair has said he will quit within a year, but there had been calls for him to go by next May at the latest.
Mr Johnson said the fact Mr Blair said he would focus on Middle East troubles before stepping down "suggests he's not thinking about a couple of weeks".
And he agreed, during an interview on BBC Radio 4's Today, with the suggestion that Mr Blair would stay on longer than many had expected at the start of the party conference in Manchester.
He said: "If the prime minister says: 'I want to use the rest of my time to try to resolve the Middle East problem in the same way we tried to tackle the Northern Ireland problem', I think it suggests he's not thinking about a couple of weeks. It's a big problem.
"But I really think people now are saying: 'Tony, the date you step down is a matter for you and it would be crazy to name a date."
'No more goodbyes'
His message was echoed by International Development Secretary Hilary Benn, who said Mr Blair's speech had removed pressure on Mr Blair to go immediately.
"After the frankly less than wonderful events of the last three weeks... the party now recognises we now owe it to Tony Blair to give him the time and space to go at the moment of his own choosing," said Mr Benn.
But backbench MP Gordon Prentice said: "He walked on water again yesterday, but the reality is that he cannot go on.
"And after yesterday's valedictory speech I find it difficult to believe he can make the same speech again in the spring, in February, because the party has it's spring conference then, and he can't do it twice."
Later, Mr Johnson, one of the possible contenders to succeed Mr Blair, told the conference he wanted to improve the experience of children in care saying the state too often showed a "chill indifference".
"Instead of bringing them up, we let them down," he said, promising unveil plans next month to make the state a "good parent".
Earlier, the conference heard from poverty campaigner Bob Geldof, who called for more aid funding in next year's comprehensive spending review.
Ex-US President Bill Clinton paid glowing tributes to Mr Blair and Mr Brown during a speech to conference which also warned that Labour's biggest problem was that people would take their achievements for granted.
But it has not all been plain sailing with the Labour leadership suffering a double defeat.
It lost the first vote when delegates backed a motion demanding the government provides more money for council houses "as a matter of urgency".
And the party hierarchy suffered a second blow when a motion criticising health reforms and calling for a review of the role of private firms in the NHS won support.
During that debate Dave Prentis, leader of public service union Unison, accused the government of pursing a gratuitous privatisation agenda "driven by dogma".
Mr Prentis urged delegates: "Set the clear red line between us and the Tories: this is their agenda, not ours."
There was angry heckling when the conference chairman turned off Mr Prentis' microphone, saying he had been warned he had gone over his allotted time.
Although the defeats are an embarrassing sign of the mood within the party at the policy, the votes do not actually mean the policy has to change.
But Health Secretary Patricia Hewitt said the reforms were putting the patients centre stage.
"After 60 years when the NHS has always used different providers it would be just as wrong to say no private involvement in the NHS as it would be to say only private involvement," she argued.
"Of course there are limits to the role of the markets in the NHS."