Martin Kettle thinks Labour MPs should tell him: "In the name of God, go." The Observer, slightly more charitably, thinks he should now focus on trying to devote himself to one or two core policy areas, in the hope that, should he lose in 2010, he will still be remembered for something other than being one of the shortest serving Prime Ministers in modern history.
So what's my take on it? Here's what I wrote in my weekly column in yesterday's Newcastle Journal.
Amidst the long list of disasters to hit Gordon Brown and New Labour during the course of local election night and after, it is hard to say which will have hurt the party the most.
Was it, perhaps, the loss of more than 300 councillors, or the Labour national share of the vote plunging to its lowest level since the days of Harold Wilson’s premiership?
Was it the party’s dismal performance in its so-called Northern “heartlands,” including the loss of Hartlepool, the continuing erosion of its position in Newcastle, and the Tory victory in North Tyneside?
Or was it possibly the humiliation of having your newly-appointed General Secretary resign before he has even taken up his post?
To my mind, it will have been none of those things, so much as the realisation that all the hopes of revival under a new leader that the sustained the party faithful during the latter years of Tony Blair have now been blown out of the water.
Make no mistake, this is as bad as it gets for Mr Brown, short of being dragged out of Downing Street feet first by David Cameron in May 2010.
As the pundits have not been slow to remind us, the last time Labour did this badly in a set of local elections was in 1968 when The Beatles were at No 1 and Flower Power was all the rage.
A more recent and more ominous historical parallel for Mr Brown is the 24pc share of the vote secured by John Major in 1995, two years before Mr Blair turfed him out of Number 10.
Is it bad enough for the Prime Minister to lose his job over? Well, it would be very easy for me to sit here and churn out a speculative piece about the potential runners and riders in a Labour leadership contest.
But in truth, it would be somewhat disingenuous. The fact is, I don’t detect any appetite in the party for another leadership change, and I don’t as yet detect any such stirrings in the political undergrowth.
Sure, some people are once again attempting to talk up the leadership chances of South Shields MP and Foreign Secretary David Miliband - just as they were doing this time last year.
But he will have none of it, and neither will leading backbench Blairites such as Darlington MP Alan Milburn, although it has to be said he would have little to lose by trying.
As an aside, it is now clear that the Brownites made a serious strategic error in “hoovering-up” the votes of so many MPs last June that the left-winger John McDonnell was unable to get his name on the ballot paper.
Had Mr McDonnell been allowed to stand, Mr Brown would have won an easy victory and been able to swot away all those jibes about being an “unelected” Prime Minister.
Even better would have been a serious challenge, from the likes of John Reid or Charles Clarke, if only for the fact that it would have forced Mr Brown to set out his confounded “vision.”
I can only imagine they concluded it would have been a waste of their energies to take part in a contest that ultimately would only have strengthened the hated Gordon.
So there is, at least, the consolation for Mr Brown this weekend that, for good or ill, the party remains committed to going into the next election under his leadership.
But the continuing support of his party will be of little use to the Prime Minister in the longer term if the country has already decided that he is a liability.
In the wake of the credit crunch, there has been much talk of the need for an experienced economic helmsman to steer us through the choppy waters, but on Thursday night’s evidence, that argument is wearing thin.
It seems to me there are now just as many people who blame Mr Brown for the economic mess than there are people who think he is the best person to get us out of it.
And it’s not all about rising fuel bills and collapsing house prices. What is really harming Labour, in my view, is the feeling that they have run out of steam, that there is no longer any good reason to vote for them.
Less than a year ago, Mr Brown stood on the steps of Downing Street and used the word “change” 27 times as he set out his personal manifesto for power – but what has it actually amounted to?
Essentially, it has meant a greater emphasis on constitutional reform, the scrapping of the Manchester supercasino plan, tougher talk on cannabis, and a hospital deep clean.
They are all good things in themselves, in my view. But a programmme for government they do not make.
It is this paucity of vision, above all, that Mr Brown needs to address in the “relaunch” that he is now apparently preparing in the wake of Thursday’s election carnage.
Key to it will be the draft Queen’s Speech, which is set to be unveiled at the end of the month and which is expected to include measures on welfare, education reforms and involving the community in tackling crime.
But whatever its contents, it must demonstrate some innovative fresh thinking which captures the public’s imagination and which gives the government a new raison d’etre.
Above all, it must be authentically Labour, something which the public will see as fair and just and not simply as another piece of political posturing designed to out-tough the Tories.
This week, Lib Dem leader Nick Clegg taunted Mr Brown by quoting Neil Kinnock’s “grotesque chaos” speech at him, in relation to the closure of thousands of post offices up and down the land.
Mr Clegg is right. Real Labour governments do not close the post offices on which deprived and isolated communities depend, any more than real Labour governments put up taxes on the poor.
That New Labour has tried to do both these things is symptomatic of a government which lost its moral compass a long time ago and, despite Mr Brown’s pretensions to the contrary, has failed to recover it.
Unless it can do so, and fast, then Thursday 1 May 2008 will come to be seen as the beginning of the end of the long Labour hegemony.