Two days into the great Brexit debate, a Tory MP called Sir Robert Syms rose to his feet to address the House of Commons. Syms is not especially well known outside his constituency of Poole in Dorset and in normal times stays loyal. But at 6.40pm on Wednesday, with few MPs remaining in the chamber, the unsung 62-year-old announced with a heavy heart that he could not back the prime minister over her Brexit deal.

“I am unhappy about voting against my government,” he declared. “I have been a member of parliament for more than 20 years. Since coming into government in 2010, I have voted against the government only once. This will be the second time. I hope that I never have to do it again because I believe that politics is a team game and I want my team to win and I want the prime minister to do the best for our nation. Unfortunately, though, I am a Conservative and unionist, and the backstop is something that I cannot accept.”

For several weeks Theresa May has been holding private meetings in Downing Street and the Commons with MPs like Syms. She has used all her powers of persuasion to try to win them around ahead of Tuesday’s historic “meaningful vote” on her deal.

Tory whips have tried to cajole their wavering backbenchers day and night, arguing the case for the May deal and reminding the more ambitious among them where their best career interests lie. Two weeks ago May made the campaign a national one – writing directly to the people of Britain and asking them to put more pressure on their MPs to support her.

A special Tory website called Back the Brexit Deal was launched by the party to rally grassroots Tories behind the cause, with limited success. Constituency chairmen were lobbied heavily, too.

Ominously for the prime minister, however, the ultra-hard sell has achieved almost nothing. Some Tories even think it has had the reverse effect to that intended – making people focus in more detail on her deal than they would have done, only for them to conclude they could never back it.

One senior Conservative said the party machine had deployed every resource it could muster but had failed totally. “Whether it is our backbenchers, or the party faithful, or the public, it is the same. If anything, I think the whole ‘going to the country thing’ has made things worse.”

By this weekend more than 100 backbench Tory MPs had declared themselves ready to vote against May’s deal. Surveys of Tory members show they are against, too, by a big majority.

After a dreadful week in which May’s government was found to be in contempt of parliament for refusing to publish the full legal advice on Brexit, the chief whip, Julian Smith, has been telling No 10 that it is on course for a huge defeat.

Some cabinet ministers still loyal to the prime minister fear she will struggle to survive the humiliation of a three-figure loss on the most important issue to have faced parliament in decades, and are pleading with her to come up with a plan B to avoid total humiliation – or to buy time by delaying the vote. But they seem to have no idea of what she can do that would swing enough hardline Tory opponents of her plan behind it at the eleventh hour.

The EU, meanwhile, insists the deal cannot be modified. Brussels says any attempt by the UK to seek substantive changes over the backstop or anything else at an EU summit in Brussels this week will be futile.

More junior members of the government are rumoured to be ready to quit before Tuesday because they can’t live with the deal as it is.

With two days to go, there is no sign May is ready to delay, change course or blink at all. One senior Tory said: “If she has a plan B, no one knows what it could be. It looks like a crisis with no solution. She seems ready to march on into the gunfire.”

Labour is keen to make out that Tuesday’s vote will be tighter than everyone expects. It is desperate to promote this view in case May limits a defeat to far less than 100. If she did that she might just be able to take some comfort and argue to Brussels that with some extra concessions in her pocket she could take an improved deal back to the Commons before Christmas and get it through second time around.

But with all but a handful of the 257 Labour MPs, the entire block of 35 SNP members, all but one of the 11 Liberal Democrats, and the 10 DUP members set to vote against it – and more than 100 Tories on record as being opposed – the arithmetic points to a far worse outcome for the prime minister.

Today there is yet more bad news for May as the all-party Commons select committee on Brexit publishes a report on her deal, unanimously agreed by members, including its 10 Conservative MPs, which concludes that after 20 months of negotiations it “fails to offer sufficient clarity or certainty about the future”.

It adds: “There are no realistic, long-term proposals from the government to reconcile maintaining an open border on the island of Ireland with leaving the single market and customs union.”

While the committee’s role is not to advise MPs how to vote, the tone of its conclusions provide a snapshot of informed cross-party parliamentary opinion. Its chairman, Labour’s Hilary Benn, says the deal “would represent a huge step into the unknown”.

Since arguments over the UK’s future relationship with the EU began to grip Westminster more than a quarter of a century ago, the biggest, most important parliamentary votes have tended to be dramatic because they have been on a knife-edge.

In July 1993 John Major lost a vote on the Maastricht treaty by just eight votes and then called a vote of confidence of the House. It is a measure of the crisis engulfing the prime minister and the country more than 25 years on that a defeat on that scale on May’s tortuously negotiated deal for leaving the EU would be regarded by everyone in Downing Street as a triumph beyond their wildest dreams.