It would make things very interesting. But it won't happen. This is not Australia.
Little is safe as houses.
It is a red button call and MPs are particularly sensitive about the polls before an election - especially those relying on list seats to get back in. Fights for survival can make people do stupid things.
But Labour's MPs know the disunity and instability such a scenario would create would be a greater torpedo to its chances than a leader who hasn't managed to woo the voters to the point they might like.
There are situations in which a leadership change so close to the election might be desirable. That is when a party knows it will get a pasting, and another leader is brought into to try to hold up the vote as much as possible rather than risk complete collapse.
That was the rationale behind Mike Moore taking over from Sir Geoffrey Palmer in 1990 and Kevin Rudd rolling Julia Gillard to lead Australia's Labor Party in 2013.
That scenario only comes when a party's vote is in danger of a big collapse. Things are not at that point for Labour.
Labour would have had more cause to invoke the clause before the 2014 election when its vote was sliding down from the 30s and into the 20s under David Cunliffe.
It might have been tempting - but the MPs could not risk the fallout from the wider party membership which anointed Cunliffe in great numbers.
MPs are certainly thinking about the next leader if Little can't pull it off and they remain in Opposition.
Little might even survive if Labour's vote rallies, especially if the fickle thumb of the Emperor, NZ First leader Winston Peters, is the reason Labour is not in government rather than Labour's own polling.
If not, the name with the most traction is Jacinda Ardern - whether she wants it or not - and Grant Robertson as deputy - the reverse from the ticket order Robertson stood on in his two pitches to be leader.
There is another problem to the theory Little will be rolled. It would require a willing and able replacement.
On the able front, very few of the current MPs would be able to step in at such a late stage, straight into the white heat of a campaign. Grant Robertson, Phil Twyford and David Parker could cope but would likely do no better than Little.
Ardern does not yet have the breadth of knowledge and experience required, especially on economic matters which are always a crux of a campaign.
On the willing front, things are even more dire. Nobody wants to be a kamikaze candidate.
For the good ship Labour it will remain 31 souls on board, Little safe.