The prime minister was urged to postpone the crucial vote next Tuesday, as about 90 Conservatives are expected to rebel.
It came as supportive MPs suggested that details surrounding the Northern Irish backstop be changed – in the hope they would help the deal pass in parliament.
Meanwhile, prospects of a showdown between Mrs May and Labour leader Jeremy Corbyn were dashed as ITV withdrew its offer to host a televised debate.
The countdown is ticking closer to Tuesday’s “meaningful vote” on the Brexit deal, with MPs completing their third day in five to debate it.
But the lack of wavering backbenchers coming out in Mrs May’s favour seemed to rattle her supporters.
Sir Graham Brady, who chairs the influential 1922 committee of Tory MPs, said most people wanted to “see this process moving forward”.
But he admitted: “I don’t think there’s any point in ploughing ahead and losing the vote heavily.”
The DUP’s Ian Paisley also quipped that “nothing so concentrates the mind like a hanging”, warning that “the gallows are being built”.
He asked International Trade Secretary Liam Fox about reports that ministers were considering postponing the vote, or if “the government [is] fixed on walking towards those gallows”.
Dr Fox insisted the Brexit deal offered a “balanced and reasonable approach”.
He added: “Of course [the government] will want to look for ways to give reassurance.”
Sky News understands Mrs May would struggle to delay the vote because the debate leading up to it has already started – meaning she would need to win another vote adding an amendment to push it back.
A Sky source also said the cabinet agreed the vote could not be lost by 200 votes, but that they did not agree to back delaying it at a meeting on Thursday afternoon.
In a bid to assuage Tory Brexiteers, loyalist MPs published a plan to decrease the chances of the UK falling into the backstop.
The backstop has created so many rebels because it would see some customs treated differently in Northern Ireland as in Great Britain.
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Led by Hugo Swire, the plan would give MPs the chance to vote to extend the transition period at the end of 2022 – rather than falling into the backstop.
Asked by Sky News if Downing Street had had a hand in its drafting, one of the plan’s backers said: “There are probably several cooks involved in the broth.”
The amendment will have to be selected as part of six by the Commons speaker on Tuesday morning if it is to be debated.
Former foreign secretary Boris Johnson, who has ruled out voting for Mrs May’s deal, said it was “simply not possible”.
He insisted that, under the terms of the withdrawal agreement, a joint committee would ultimately make that decision.
It was also rejected by Arlene Foster, leader of the Democratic Unionist Party, which is propping up Mrs May’s government.
“Domestic legislative tinkering won’t cut it,” she wrote on Twitter.
“The legally binding international withdrawal treaty would remain fundamentally flawed as evidenced by the attorney general’s legal advice.”
