Something unusual has started to happen. Whenever I go for lunch, dinner, a drink or a coffee with a Labour MP, they ask the same question: how would I vote, were I an MP, when Theresa May’s deal with the European Union comes to the floor of the House in a few weeks’ time?

Nearly every journalist I have asked has had some version of this experience. One parliamentary staffer, who has worked for his boss for more than half a decade, has had several conversations about the looming vote – although “it seems more like free therapy than a serious conversation”. During a recent meal I was having with a high-profile MP, a member of the public stopped to congratulate my lunch partner on their work – and the passer-by was promptly grilled about how to approach Brexit.

MPs of all parties are worried about the coming vote but the outbreak of anxiety is particularly acute on the Labour side. It has become increasingly clear that there are not enough votes to pass May’s Brexit plan with the support of only Conservative MPs, the seven committed Labour Leavers and the Democratic Unionist Party. The Prime Minister’s proposed deal involves too big a breach from the European Union and its internal market to be acceptable to pro-European Conservatives, but keeps the UK too closely bound to the rules of the bloc to be acceptable to pro-Brexit ones.

Some Tories, such as Jo Johnson, the Remainer who quit as transport minister on 9 November, oppose it twice over. First, because of the likely economic damage; second, because of the unacceptable loss of sovereignty involved in being a rule-taker but not a rule-maker.

Here’s the gamble. Voting down the proposal could mean a No Deal Brexit, or no Brexit at all. The first of these would leave planes grounded and the United Kingdom facing shortages of fresh food and medicine. The second can be achieved only by asking the British people to overturn their decision in the 2016 referendum. Jo Johnson is the latest pro-European Conservative MP who has come round to the idea of a referendum on the terms of Brexit. For him, there would be a three-way choice: May’s deal, staying in the EU, or leaving without a deal.

Other Conservatives go further than Johnson, as the former minister Philip Lee did forcefully at the party conference in October, by saying that the Brexit mandate is impossible to honour because it was based on a series of untruths. Only a second, honest vote, can allow the country to move on, whether with Brexit or without it. (In Jo Johnson’s case, loyalty to his older brother Boris probably contributed to his decision to eschew that particular line of argument.) Most MPs in this group of Remain Conservatives plan to vote against May’s deal and then plan for a second referendum.

But not all pro-European Tories favour that course. For some, it is a simple matter of tactics: they don’t believe that a second vote can be won and therefore don’t see the point. Others are against referendums full stop: “One was too many,” sighed one MP. And for another referendum to be fair, it would have to include all three options, including No Deal. What’s the point of a representative democracy if MPs allow the public to vote for food and medicine shortages?

And so, a new tendency is gaining power in the Conservative Party. It follows the path set out by Stephen Hammond, MP for Wimbledon, and Nicky Morgan, the Treasury select committee chair. They are lobbying for the only form of Brexit that could pass the Commons: joining the European Economic Area (EEA) and remaining in a customs union but leaving the political project of the European Union.

That faces opposition from other pro-European Tories, who argue that a People’s Vote would be better because an EEA end-state would not fulfil the referendum’s promise of “taking back control” of laws and borders.

There are similar agonised debates taking place among Labour MPs. The party leadership has a firm plan: vote against May’s deal in the hope that her defeat would somehow trigger an early general election. Labour advocates of a second vote have a strategy, too: they want to vote against May’s deal and believe that, in the ensuing mess, the only option that would emerge is a People’s Vote.

But there is a third group of MPs who don’t believe that there is a plausible way for the opposition to force an election because of the constraints of the Fixed Term Parliaments Act (the government would essentially have to call one, which would be a high-risk move having lost a defining vote). This group doubts that a People’s Vote is even possible – the timetable is very tight and many of their own colleagues are against the idea – let alone winnable.

These MPs also believe that the only deal that can meet the government’s red lines – no border in the Irish Sea and no border on the island of Ireland – is a Brexit that keeps the UK in the EU single market and customs union. Voting it down is “a roll of the dice”, they say, with no guarantee that it will be followed by No Brexit (good) rather than No Deal (bad).

In any event, following such a catastrophic defeat in the Commons, Theresa May would in all likelihood be replaced as Tory leader and prime minister by a committed Brexiteer who would simply want to wait out the clock until the end of the Article 50 process in March next year. After which we would have the hardest of Brexits, and without a parliamentary vote.

Labour backbenchers know the fate of the country is in their hands – and that rolling the dice has potentially huge risks, as well as huge rewards. As a parliamentarian, you might willingly be given advice by every passer-by, but the decision looks different when it’s your name on the division list.