One minister and four government aides are among 17 normally loyal Labour MPs who have written to Tony Blair urging him to quit.
Mr Blair may now decide to give more departure details
The MPs - including junior defence minister Tom Watson - say they want an end to uncertainty.
Senior minister Hilary Armstrong later said Mr Blair would be gone by the time of the 2007 Labour conference.
Forty-nine Labour MPs have so far signed a statement saying they are satisfied with a 12-month timetable.
But others - including a group of Labour MPs elected in 2005 who are thought to be drafting their own letter to Mr Blair - want him to quit immediately.
Ms Armstrong, who is close to Mr Blair and is a former chief whip, is the first member of the prime minister's inner circle to go so far in statements about his future.
The social exclusion minister said the 12-month timescale was a "realistic date".
"The prime minister has promised that there will be a smooth and orderly transition," she said.
"The perceived wisdom, although I might have advised something differently, is that he acknowledges that by conference next year, there'll be a new leader in place."
Mr Blair last week rejected calls to use this month's Labour Party conference to name a timetable for his departure.
But his words appeared to fuel uncertainty, with normally loyal Labour backbenchers calling on him to name an exit date.
A senior Cabinet source confirmed the letter from 17 Labour MPs, all of whom entered Parliament in 2001, calling on Mr Blair to go had been sent to - and seen - by Downing Street.
The group includes West Bromwich East MP and junior defence minister Tom Watson.
Ministerial aides Khalid Mahmood, Wayne David, Ian Lucas and David Wright also signed the letter.
The Cabinet source said the letter was likely to convince Mr Blair he needed to say more about his departure plans.
Blairite MPs Chris Bryant and Sion Simon are understood to have co-ordinated the letter from the 2001 intake.
But Mr Bryant refused to comment on its contents, telling BBC Wales that if he had sent the prime minister a private letter it would be "a private matter".
A second letter from a group of Labour MPs elected last year has also been drafted but not yet been sent.
Bristol MP Kerry McCarthy said she had not yet signed the 2005 intake letter but agreed the party's troubles had to be resolved soon, with Mr Blair leaving by the spring.
Another 2005 MP, who did not want to be named, said Mr Blair was politically "wounded" and should go immediately.
But Sir Jeremy Beecham, chairman of Labour's national executive committee, said the MPs' letters were misconceived.
Mr Blair was "conscious of what needs to be done" and would ensure a new leader was in place by the time of next year's Labour conference, said Sir Jeremy.
The day began with minister David Miliband telling BBC Radio 4's Today programme he agreed with the "conventional wisdom" that Mr Blair would step down in 12 months - the most senior minister at that point to name a departure date.
Meanwhile, a leaked memo suggesting a farewell tour to promote the "triumph of Blairism" was published by the Daily Mirror.
The memo, reportedly drawn up by a group of his allies, including his pollster Philip Gould, says: "He needs to go with the crowd wanting more."
Downing Street says neither Mr Blair nor any senior No 10 staff have seen the memo.
The reports come as a Populus poll suggested the Conservatives would have a strong lead over Labour whether Mr Blair stayed on, or was replaced by Gordon Brown or John Reid.
The poll of 1,504 people also suggested 30% of Labour voters and 51% of the general public wanted Mr Blair to step down this year.