Several dozen rebel lawmakers are growing restive and have discussed attempting to replace May with a strongly pro-Brexit politician such as former Foreign Secretary Boris Johnson, a fierce critic of May's Brexit blueprint.
The lawmakers, part of the European Research Group (ERG), an anti-EU grouping in May's Conservative party, met on Tuesday night and openly discussed May's future as leader, the BBC said citing an unnamed source.
"We can vote down the bad Chequers proposals on Monday and support the government in a vote of confidence on Tuesday".
"I have long said, and repeated again and again, that the policy needs to be changed but I am supporting the person", he said.
A proposal hammered out by May's Cabinet in July at the prime minister's Chequers country retreat proposes keeping the United Kingdom aligned to European Union regulations in return for free trade in goods.
"If the currency market is anything to go by, the markets are too pessimistic about the possibility of a no-deal Brexit", said Mike Bell, a global markets strategist at JP Morgan Asset Management in London. He has beforehand indicated that settlement would be foremost by mid-November to enable time for the foremost ratification procedures.The Brexit deal is to embody the so-known as divorce terms, as neatly as ushering in a 21-month transition duration.
Former Brexit Secretary David Davis, who quit the cabinet in July over the proposals, told reporters he expected May's government to change course on Brexit after an informal meeting of European Union leaders in Salzburg next week.
"You have seen over the summer I think an intensification in the talks - that is obviously something which we called for - and you have seen progress continuing to be made in relation to that withdrawal agreement", May's spokesperson said.
Even a small rebellion inside May's party on a vote over a final deal could spell the end of her minority government and throw Britain's exit into chaos. The rift deepened this week with Johnson comparing May's plan to a "suicide vest" on Britain's constitution.
TUC general secretary Frances O'Grady said: "Whether it's through a general election or a popular vote, Mrs May should take her deal on the terms of Brexit and put it back to the people".
A number of MPs told how they had submitted letters of no confidence to Sir Graham Brady, chairman of the 1922 Committee, and others discussed plans to follow suit. Under Conservative rules, a leadership election is triggered if 15% of Conservative lawmakers, now 48 of its 315 members of parliament, demand a vote of no confidence.
The EU's chief Brexit negotiator, Michel Barnier, has sounded more hopeful of resolving the issue, offering to be flexible in his approach to agreeing the so-called backstop plan to avoid a hard border. One of those present said opposition to her leadership has hardened over the summer.