MPs could damage faith in democracy by failing to back Theresa May’s deal on Tuesday night, the environment secretary, Michael Gove, has said, quoting the Game of Thrones slogan “winter is coming”.

Gove, a leading figure in the leave campaign during the 2016 referendum, said he believed the public would see a vote against the deal as MPs attempting to frustrate Brexit – though most of May’s most vocal opponents in her own party are hard Brexiters.

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“If we don’t vote for the deal tonight, in the words of Jon Snow, ‘winter is coming’,” Gove said, citing the motto of the prominent Stark family in the HBO fantasy TV series, which predicts the coming of a frozen army of the undead.

“I think if we don’t vote for the deal tonight we will do damage to our democracy by saying to people we are not going to implement a Brexit, and the opportunity that all of us have to live up to our democratic obligations is clear.”

May is on course for a crushing defeat in the House of Commons inflicted by her own MPs. Guardian analysis pointed to a majority of more than 200 MPs against the prime minister, more than 100 of her own backbenchers.

Overnight two more MPs, including the former international trade minister Greg Hands, said they could not vote for the deal as it stood.

Gove refused to predict a victory for May but said the real risk for Tory MPs was that a defeat would mean Brexit could not be delivered. “We know there are people in the House of Commons and outside who have never made their peace with this decision, who want to overturn it,” he told BBC Radio 4’s Today programme.

The environment secretary also defended the backstop arrangements to prevent a hard border in Northern Ireland, which are opposed by many Tory Brexiters and the DUP.

“I think the whole point about the backstop is that it’s deeply uncomfortable for the EU,” he said. “The European Union said at the very beginning of this process that there would be no cherry-picking, the four freedoms of the single market were indivisible.”

Instead, Gove said, the government had “picked a whole bowl of glistening cherries” including free access to the European market with no tariffs and no quotas, but without paying into the EU budget or accepting freedom of movement. “We are in a stronger position in the backstop,” he said.

Brexiters have been particularly angered by the backstop, an insurance arrangement to keep the UK in an effective customs union until a solution is found to prevent a hard border in Northern Ireland, because it does not have a firm end date and cannot be exited unilaterally.

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On Monday, May issued one final call to parliament to back her, urging MPs to “take a second look” at her deal, but there was little evidence in the debate in the House of Commons that followed that many had been convinced.

The attorney general, Geoffrey Cox, will open the final day of debate on Tuesday, which will be closed by May herself. Voting is set to begin on a series of amendments from 7pm. Downing Street has suggested the prime minister will make an immediate statement after the vote result is announced.

The Labour leader, Jeremy Corbyn, is expected to call a no-confidence vote in May shortly after the defeat. However, a Labour source said even if that vote were lost, it would not mean an immediate endorsement to campaign for a second referendum.

The source said that the policy agreed by Labour conference identified a public vote as one of the options but said it was not necessarily preferred. “Obviously we will judge how to deal with the options and get the best result for the country on the basis of what happens in parliament,” the source said.

The shadow Brexit secretary, Keir Starmer, spelled out the options, which he said included pushing for a different Brexit deal that could command support.

“We need to create the space for that discussion about the credible alternatives,” he said. Pressed on his preference, he added: “We can’t have no-deal and therefore we need to find a majority for something else. Our party conference set out the option of a public vote, a second referendum, and obviously that has got to be discussed.”

The Labour MP Hilary Benn bowed to pressure from party colleagues on Tuesday morning and pulled his amendment to the deal because a victory may have masked the true scale of the prime minister’s defeat on the deal.

The amendment, which would have rejected May’s deal and a no-deal Brexit, would have made it impossible for the vote on May’s deal itself to go ahead if it had passed.

Government whips had suggested MPs who hoped to spare May the humiliation of a three-figure defeat on her Brexit deal should vote for the amendment submitted by Benn.

Another amendment tabled by the Tory backbencher Andrew Murrison which aims to put a “sunset clause” on the backstop arrangements in the withdrawal agreement is also gathering steam among Tory loyalists.

The amendment has been signed by a number of senior Tories, including Sir Graham Brady, Damian Green and Robert Goodwill, suggesting it has some tacit whips’ support.

The EU has thus far refused to countenance putting any exit date in the backstop arrangement but the amendment could act as further proof that the deal will not pass parliament without one.

The amendment will not pass the Commons because it does not have Labour frontbench support, but No 10 is likely to watch to see how much support the ploy will attract.