If Theresa May is to get her Brexit deal through parliament, these are the groups she will have to convince:

Diehard Brexiter Conservative MPs

They were always going to be the trickiest group to pick off, and amid significantly varying estimates of their numbers – anything from fewer than 40 to 80-plus – May knew some rebellion was inevitable over any deal she was likely to bring back.

The trick was always going to be to reduce the size of the rebellion, and hope MPs from other parties could fill the gap.

May’s task has been made all the trickier since the European Research Group (ERG) of strongly pro-Brexit Tory MPs moved from campaigning against her Brexit plans to actively seeking to depose her as prime minister.

Led by Jacob Rees-Mogg, the ERG has urged Tory MPs to send letters of no confidence in May in sufficient quantities to trigger a leadership challenge and, they hope, replace her with a more Brexit-committed prime minister.

The bad news for May is that if an MP has called publicly for you to go it is hard to see any realistic tweak to the Brexit plan that would get them back on side.

The much better news for her is that the attempted coup has revealed how relatively weak the ERG is, the attempt fizzling out when not enough MPs heeded its call to reach the 48 letters needed.

That arguably takes May back to where she was at the start – having to factor in a relatively small if influential group of irreconcilables into her Commons mathematics.

Other Tory MPs

It is arguably a bit misleading to lump together all the non-ERGers, as their Brexit sympathies range from the broadly supportive, to diehard remainers such as Anna Soubry, who would most likely oppose any departure deal.

As such, May has to once again present her Brexit plans as different things to different people, playing off each group’s aspirations and fears as best she can. A big part of this is likely to be based on using the vagueness of the political declaration on a future trading relationship as something on to which people can project their own ideas as to how it might play out.

For the more centrist Tories, May’s pitch will be her standard one: this is the only deal in town; it delivers the basics of what leavers voted for; block it and you risk all manner of chaos, from a leadership challenge to a general election or a no-deal departure.

When addressing her remain-minded MPs, May will seek to play up the softer elements of the deal, such as continued alignment with the EU, as well as raise fears over what she will pitch as the alternative: no deal.

She could face an obstacle in this respect if some remainer Tories decide they might welcome the chaos of a rejected deal, seeing it as a way to potentially bring about a second referendum.

DUP

May and her negotiators have spent many hours, days and weeks over the past year and a half trying to placate the party she relies on for her majority. But it appears to have been to no avail. The DUP’s position has been hardening from the moment the 585-page withdrawal agreement, containing the Irish backstop, dropped this month.

The DUP leader, Arlene Foster, said explicitly on Saturday that her party intended to vote against the deal, not just abstain.

Tory whips will no doubt stress the limited, “de-dramatised” nature of border checks and insist Stormont, as and when it gets up and running, will have some say in how EU rules are implemented in Northern Ireland if the backstop is invoked.

Downing Street’s strongest argument is that both sides have committed to pressing ahead with trade talks in the new year in the hope the backstop will never be needed; but the DUP does not appear to be in the mood to be persuaded. Its 10 MPs seem to be beyond May’s reach.

Labour MPs

Earlier in the autumn, Conservative whips were confident May’s deal would scrape through parliament with the help of a dozen or more Labour rebels – perhaps up to 30.

As well as a small core of openly pro-Brexit MPs, such as Kate Hoey and Graham Stringer, they hoped a swath of others from leave constituencies would back the deal rather than appear to be “blocking Brexit”; and a third group of centrists would support the government, rather than risk the economic disruption of no deal.

However, the newly rehabilitated cabinet minister Amber Rudd said last week she did not believe parliament would allow no deal to happen and Labour plans to table amendments to the meaningful vote to make it impossible.

Taking it off the table would give wavering MPs a free pass, without the fear of unleashing chaos; and many of those centrists that Tory whips were targeting are now shooting for a second referendum.

Perhaps more importantly, some of those Labour MPs who had been most wary of rejecting the prime minister’s deal, including Wigan’s Lisa Nandy and Gareth Snell in Stoke Central, have now suggested they will not vote for it.

Nandy highlighted the vague nature of the 26-page political declaration; other MPs in leave seats say they are hearing on the doorstep that even Brexit voters are not enthusiastic. Even Hoey appears likely to join Labour in the no lobby.

The public

As with her own MPs, May has to accept any PR pitch is to an extent a damage-limitation exercise, with significant percentages of the population never likely to be reconciled to her plans, not least the 700,000 or so people who marched in favour of a second referendum.

The government is certainly thinking hard about how to put out the message that May’s deal is both inevitable and the only grown-up conclusion to 29 months of post-referendum arguments.

This month a leaked memo supposedly setting out a sales pitch to the nation – dismissed as unofficial by Downing Street – laid out a schedule in which business leaders and foreign dignitaries were teed up to endorse May’s proposals.

As with all the PM’s current Brexit sales pitches, the tone looks likely to be somewhat less elegiac than the sunlight uplands of unfettered prosperity set out by some leave campaigners, with the main message likely to be: this deal isn’t too bad, let’s get it over with.

To an extent, this sense of ennui might be May’s greatest asset in selling her plan to the nation.

Speaking on Sunday, her foreign secretary, Jeremy Hunt, spoke of what he said were a significant group in Brexit Britain: those he termed the “Bobs” – people “bored of Brexit”. These are the people who might just accept May’s proposal because it finally brings the process to an end.