Harold Wilson is not a Labour prime minister anyone much quotes these days, but he did leave behind some useful observations and not just the now dated one about a week being a long time in politics. “The Labour party is like a stagecoach,” he once remarked. “If you rattle along at great speed, everybody inside is too exhilarated or too seasick to cause any trouble. But if you stop, everybody gets out and argues about where to go next.”

Since Jeremy Corbyn became the head coachman, Labour has certainly rattled along, exhilarating many of its members and causing a sensation rather worse than seasickness to a lot of the party’s ill-looking MPs. One by one, the major institutions of the party have been captured by Corbynism: the leadership, the membership and the national executive committee have all been taken in its grip. Never before in the history of the party has its left been so utterly dominant.

The party’s strong, albeit still losing, performance in last year’s election enhanced the feeling that they had the wind at their backs. In the wake of Mrs May’s self-inflicted debacle, even some Tories began to talk about a Corbyn premiership as if it were inevitable.

You hear less of that today. Rather than moving at great speed towards power, the Corbyn stagecoach has got rather bogged down. Heady predictions made in the wake of the election that they would be in power by now have not materialised. Doubts about what will happen at the next election have begun to creep into the thoughts of even some devoted Corbynites.

Labour’s poll rating is stuck in a rut. The party’s position is not awful, but nor is it exactly confidence-inspiring for those who yearn for a Corbyn government. Of the 25 most recent polls, 16 have suggested a modest advantage to the Tories, a surprise when the Conservatives are afflicted with so many problems of their own and not where you want to be as an opposition to be truly confident that power is there for the taking. Despite all the best efforts of the Conservatives to make themselves hideously unattractive to the electorate, the Tories are still edging it. As for leadership, Theresa May polls negatively, but not as badly as Labour’s rival candidate for the premiership.

The knee-jerk response to this from some Corbynistas is to say that the polls can’t be trusted. Maybe. Maybe not. The pollsters have tried to adjust for the mistakes that they made at the last election, but we won’t really know whether they’ve corrected accurately until we see the result of the next one. If the polls are as entirely rubbish as some Corbynistas maintain, that would raise the question why the Labour party still commissions quite a lot of private polling. If polls can’t tell you anything useful, why are they wasting the party’s money on them? The shrewder members of the shadow cabinet and the more thoughtful members of Mr Corbyn’s inner circle do worry about the broad message of the polls. They ask themselves why they haven’t moved decisively ahead of a government in so many extremely visible difficulties.

This is the first time in McDonnell's life that he has been lambasted by other Labour MPs for not being left wing enough

Like many a populist movement, the Corbyn revolution has been self-fuelled by its sense of relentless forward progress; a feeling of historical inevitability about its eventual victory. Momentum was named such for a reason. The optimistic idealism of many of its younger recruits has been one of the more attractive features of Corbynism. The belief that the movement was unstoppable kept supporters enthused and enemies frightened. That feeling has been dissipating over recent months, like a slowly deflating balloon.

The halt in what was supposed to be an inexorable march on power is triggering questions about where the party ought to be going in terms of policy and its electoral appeal. One symptom of that is Labour’s confused and divided response to budget tax cuts for the better-off. This set off a backbench rebellion and revealed some of the strains in the relationship between the Labour leader and his shadow chancellor, John McDonnell. Allies and friends during their decades on the parliamentary margins, they have generally done a very good job of containing or masking their differences over the past three years. So when a split between them is exposed to public view, something serious is up.

The shadow chancellor took the line that Labour should not oppose the government’s plan to raise the higher-rate tax threshold, a move that gives the largest cash benefit to some of the better-off. Mr Corbyn initially took a contradictory line, attacking the Tories in characteristic manner and language for “ideological tax cuts”. In the end, Mr McDonnell’s approach prevailed when it came to deciding how Labour would vote on the budget, a stance that then triggered a rebellion by Labour MPs. Looking at some of the rebel names, which included Liz Kendall, Yvette Cooper and Margaret Hodge, they must have been a bit surprised to find themselves voting to be more “socialist” than Labour’s current management. This must be a career novelty for the shadow chancellor: the first time in his life that he has been lambasted by other Labour MPs for not being left wing enough.

Facebook Twitter Pinterest John McDonnell believes Labour has a once-in-a-generation chance to form the radical left government that they have spent decades dreaming about. Photograph: Christopher Thomond/The Guardian

It is a bit crude to characterise the divide between the two men at the top as a clash between the ideological “purism” of Mr Corbyn and the compromising “pragmatism” of Mr McDonnell, labels that over-damn and overpraise them both. Yet there clearly is a difference of approach here, even if it is essentially about tactics, ambition and temperament. One of the shadow cabinet once remarked to me that both men have been “on a journey” as they adjusted from growing grey in the wilderness to becoming the two most significant figures in the Labour party. I think it fair to remark that Mr McDonnell’s journey has been the more interesting one. This is not to say at all that he has abandoned his convictions. He will still talk happily about his admiration for the works of Karl Marx and has never renounced his ambition to “overthrow capitalism”. If he ever gets to the Treasury, he will be the most leftwing occupant of the office in more than 60 years, arguably ever.

The difference is that Mr McDonnell has devoted more time and energy than Mr Corbyn to thinking about how they would try to put their domestic programme into practice. The shadow chancellor will go and talk to business audiences, and even seems to relish the experience, while the Labour leader remains as allergic as always to engaging with any group that might take him out of his ideological comfort zone. The shadow chancellor is more palpably hungry for power. He believes they have a once-in-a-generation chance to form the sort of radical left government that they have spent decades dreaming about and that goal should be their relentless focus. This is why Mr McDonnell was so furious that Mr Corbyn allowed Labour’s summer to be devoured by the ugly furore over antisemitism, drowning out anything that the party had to say about the economy or any other subject.

I think it is also reasonable to say that Mr McDonnell is better at maths than Mr Corbyn. This means he has been thinking harder about the coalition of voters that Labour will need to assemble if the party is to win the next election, rather than lose yet another one. Justifying the stance he took on the budget, the shadow chancellor observed that the beneficiaries of the tax changes would include better-paid workers in the public sector, such as headteachers. Labour did very well among public-sector professionals as a group at the last election and the shadow chancellor wants to hang on to their support.

This wrangle about tax is significant because it points to a larger argument within Corbynism about what they should do next. In the wake of the 2017 election, Labour’s above-expectations result was widely attributed to its manifesto, a document that the shadow chancellor repeatedly refers back to. But that manifesto gets more whiskery with each passing day. The context of the next election will be different, perhaps dramatically so. Should Corbyn Labour largely stand pat or should it prepare an even more leftwing offer for the next time the British people are asked to choose a government? That argument might be avoided if Brexit collapses the government, which is one of the reasons why the Labour leadership sounds desperate for an early election. Otherwise, this debate is going to become increasingly lively.

Just as Harold Wilson predicted, when the stagecoach stops rattling along, everybody gets out and argues about where to go next.

• Andrew Rawnsley is an Observer columnist