The last time Theresa May took to the road in an attempt to convince the great British public to back her on Brexit, it didn’t go that well – her majority was wiped out, and with it any hope of “strong and stable” government.

Yet with two weeks left before “one of the most significant votes that parliament has held for many years”, as the prime minister put it on Sunday, Downing Street believes a direct appeal to voters will help get her controversial deal over the line.

May will travel to Wales, Scotland and Northern Ireland in the next few days, in what she has called a “campaign”, to sell the deal directly to the public – squeezing in a G20 summit with world leaders in Buenos Aires at the weekend, before another flurry of public appearances in England next week.

No 10 believes there is already considerable sympathy for the beleaguered prime minister, who has doggedly ploughed on with the negotiations in the face of cabinet walkouts, cackhanded coup attempts and “secret” cabinet plots.

And they are counting on the fact that while polling shows voters are unenthusiastic about the deal, they are also keen for Brexit to be over and done with. “The British people don’t want to spend any more time arguing about Brexit,” as May put it on Sunday.

It’s MPs, not voters, who get a “meaningful vote” on the deal but May’s strategists hope that by stirring up a supportive public mood, they can force MPs to shut out the tearoom chatter in Westminster and help her to conclude Brexit.

For MPs more likely to be swayed by spreadsheets than a nebulous sense of their constituents’ preferences, civil servants will publish a hefty economic analysis of the deal on Wednesday – comparing it to the status quo, and the alternative of no deal.

Labour MPs will get their own briefing from the prime minister’s chief of staff, Gavin Barwell, and her de facto deputy, David Lidington.

Lidington gave a hint of the arguments he is likely to use in an intriguing tweet on Sunday, describing the deal as a “good compromise” between leave and remain. But one Labour MP, receiving the invitation on Monday, said they “didn’t know whether to laugh or cry”, and it was “much too late”.

Today's agreement is a good compromise. The 52% get control of laws, money, borders + out of CFP; the 48% get closer trade partnership with EU than Canada or any advanced economy + cooperation on police & security. Time for country to come together & #BackTheBrexitDeal — David Lidington (@DLidington) November 25, 2018

The government’s long-awaited immigration white paper is also expected to be published before the meaningful vote.

It will underline what May believes is one of the key selling points of her deal, that distinguishes it from the so-called “Norway-plus” approach being enthusiastically promulgated by the backbencher Nick Boles – it will allow the UK to bring freedom of movement to an end, “once and for all”.

Downing Street’s job in promoting the deal has been made all the more difficult by the structure of the meaningful vote and its aftermath, which was hammered out through a series of amendments to the EU Withdrawal Act.

MPs led by Dominic Grieve, and with the backing of the Lords, battled to tie the government’s hands, to prevent it from defaulting straight to no deal in the event of parliament saying no.

The amendment that emerged from the ensuing wrangle obliges the government to come back to parliament within 21 days – and “make a statement setting out how Her Majesty’s government proposes to proceed in relation to negotiations for the United Kingdom’s withdrawal from the EU”.

The main motivation of Grieve and his allies was to erect parliamentary hurdles the government would have to surmount before it could take Britain out of the EU without a deal.

But a side-effect may have been to give MPs the feeling they can have a free pass on the first vote, in the hope that alternatives will open up in the uncertain period that follows.

However slick the PR blitz over the next fortnight, the fate of May’s deal may well have been sealed more than a year ago. The general election radically shifted the centre of gravity in the House of Commons – but May ploughed on with her approach to Brexit all but unchanged.

As many as 90 of her own MPs are vowing to oppose the deal, at the Guardian’s latest count, as Monday’s almost relentlessly hostile reception for the deal in parliament made clear.

With hindsight, Downing Street strategists may wonder if they could have done more to shape their approach to fit the centre of gravity in parliament – but all they have left now, aside from the spectacle of the prime minister criss-crossing the country, is trying to harry, cajole and persuade MPs over the line.