May is battling for her political survival after announcing a Brexit negotiating strategy that enraged eurosceptics in her Conservative Party, who see it as a plan to keep Britain too closely tied to Brussels.
The size of the threat should become clear on Monday when lawmakers vote on amendments to legislation on the government's post-Brexit customs regime, with leading eurosceptics set to vote in favour of amendments that May opposes and back their own proposals to toughen up her exit plan.
While May is not expected to be defeated on the amendments, a high number of votes in favour of altering the customs bill by members of her party would further undermine her negotiating strategy, agreed at a cabinet meeting at her Chequers country residence this month.
"I cannot find someone who supported leave within the Conservative MPs (Members of Parliament) who is happy with the (Chequers) proposal if you talk to them in private," Peter Bone, a Conservative lawmaker and Brexit campaigner, told Sky News.
The Chequers agreement has already led to the resignations of high-profile cabinet members David Davis and Boris Johnson.
May attempted to face down would-be eurosceptic rebels by warning on Sunday that if they sink her premiership then they risk squandering the victory of an EU exit that they have dreamed about for decades.
A party meeting last week looked to have snuffed out talk of a confidence motion challenging May's leadership, which would require 48 Conservative members of parliament to initiate, and 159 to win.
But, fuelled by criticism from U.S. President Donald Trump and anger at grassroots level in the party, the sentiment against May has gained fresh momentum.
Both could speak in the debate, currently due to start at 1430 GMT and end with votes at 2100, and they may have an important influence over how many colleagues are willing to speak out.
The amendments to the Taxation (Cross-border Trade) Bill have been proposed by arch-eurosceptic Jacob Rees-Mogg. He said he did not expect the bill, or another key bill on trade due to be debated on Tuesday, to be blocked outright by the 650-member parliament.
"I'm sure Theresa May does not want to split the Conservative Party and therefore she will find that the inevitable consequence of the parliamentary arithmetic is that she will need to change it (the Brexit policy) to keep the party united," Rees-Mogg said.
"We'll have an idea of the numbers, I suppose, at 10 o'clock on Monday evening."
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)