Those names being discussed by Labour MPs as potential candidates to displace Sir Keir include some of his closest cabinet allies, especially Wes Streeting, the health secretary, and Home Secretary Shabana Mahmood.
Some also speculate about the ambitions of Ed Miliband, the energy secretary, and backbenchers including the former transport secretary Louise Haigh.
“He will fight this,” one minister said, before making reference to a key by-election in 2021 which Labour lost to the Conservatives, prompting Sir Keir to consider resigning as Labour’s leader.
“This is not a Hartlepool moment,” they added.
“He is one of only two people alive who have won a general election for Labour. It’d be madness to run against him after 17 months.”
For months now, plenty in the Labour Party have acknowledged that the government faces a likely crunch point after devolved elections in Scotland and Wales and local elections in many parts of England next May.
Labour is widely expected to do badly in those elections, but there are growing concerns from some in the party that it can’t wait until then to contemplate a change of leader.
Downing Street is aware of the potential imminence of such a threat to them.
One senior Labour MP told us: “It’s all very well to say wait for the locals, but that’s my activist base I’m sending into the gunfire. I can’t lose all my councillors.”
Another Labour source said: “The list of reasons for people to move after the Budget are growing by the day.
“If Wes is brave and moves he may well be rewarded by being prime minister by Christmas.”
The ambition of Streeting is seen with particular suspicion from some loyal to the prime minister.
A spokesman for Streeting told the BBC “these claims are categorically untrue”.
“Wes’s focus has entirely been on cutting waiting lists for the first time in 15 years, recruiting 2,500 more GPs, and rebuilding the NHS that saved his life,” he added.
The health secretary is due to do a round of interviews on Wednesday morning which were due to be focused on his plans for shaking up the NHS in England.
A government source said Downing Street “has gone into full bunker mode, turning on their most loyal cabinet members for absolutely no reason”.
“Unfortunately there is a pattern of Keir’s team briefing against his own people- they did it to Angela, Lisa, Lucy, now it’s Wes’s turn,” the source added.
“A circular firing squad won’t help the government out of the hole we’re in,” a government source said – referring to the former and current deputy leaders, Angela Rayner and Lucy Powell respectively, and the Culture Secretary Lisa Nandy.
