I suspect that "God forbid!" would be the answer of most Labour Party members to that question, but the current pressure on Harriet Harman over the dodgy donations affair means the possibility cannot be ruled out.
So of the half-dozen candidates who stood last time round, who would risk throwing their hats into the ring again? Possibly only one or two, in my view.
Harman, of course, would automatically be ruled out. So too would Hazel Blears, Hilary Benn and Peter Hain on the grounds of their disappointing performances in June.
The only candidates from this summer's race I can see fancying another run round that particular block are Alan Johnson, pipped at the post by Harman after being widely tipped as the victor, and Jon Cruddas, who came a good third on the back of a strong grassroots campaign.
Cruddas turned down the offer of a job by Gordon Brown - there is some dispute as to whether it was a party vice-chairmanship or a junior ministerial post - and so is untainted by association with any of the disasters to strike the government over recent weeks. He could well win.
Johnson would also find it hard not to stand, having come so close before. But there would, I think, be other candidates.
The demographics of the Labour Party make it almost certain there would be a woman, with Caroline Flint, Ruth Kelly and Jacqui Smith among the possible contenders in the enforced absense of Harman and Blears.
I think Jack Straw would also fancy it. He expected to be made Deputy Prime Minister, or at the very least First Secretary of State, in Brown's first reshuffle, but the Prime Minister foolishly denied him both titles. He could not deny them were Straw to become deputy leader.
The big question, though, is whether one of the disgruntled Blairites would throw their hats into the ring - Charles Clarke, perhaps, or Alan Milburn, or even Foreign Secretary David Miliband?
If so, the media would very quickly try to turn it into a leadership election at one remove, and the attractions of Straw as a "unity candidate" would become even more apparent,
Could this be Jack's big moment? Although Brown will do all he can to save Harman, I fancy the Government would actually look stronger without her, with Straw officially installed as DPM and someone else entirely - Cruddas? - in the role of Party Chair.
Then again, Michael Heseltine's appointment to the same role in 1995 was supposed to strengthen John Major. And look how that ended.