The prime minister faces a lengthy interrogation in the House of Commons when she presents herself to update parliamentarians, as is usual after a summit with other EU leaders in Brussels.
She is prepared for anger from all sides for her handling of the negotiations.
Theresa May will explain a series of areas in which the talks have progressed only in the last three weeks, on topics ranging from Cyprus to Gibraltar and security, transport and services relations, in addition to the agreements reached previously.
"Taking all this together, 95 percent of the withdrawal agreement and its protocols are already resolved," he promised his impatient troops.
He will also take a vow not to accept the European Union's proposals effectively to put a customs border in the Irish Sea that divides Northern Ireland from the rest of the United Kingdom.
But he faces furious challenges over his agreement last week to consider extending the post-Brexit transition period from late December 2020 to 2021.
She has said that it may be necessary to avoid creating a hard border between Northern Ireland and Ireland, but Brexiteers fear that it will only catch Britain even more in EU rules and payment obligations.
The Tory unhappiness is such that some predict the amount of formal letters sent by parliamentarians who demand a contest. This week will reach the threshold of 48 to trigger a challenge.
The main critic of May, Andrew Bridgen, said on Sunday: "She has lost the confidence of large swaths of the party.
Brexit: Theresa May faces a barrage of parliamentarians in the House of Commons
"Some people have been waiting for it to get worse before sending their letters, but it can not be much worse than this."
"This week, Theresa May will discover that she is drinking in the lounge the last time and the bad news for her is that the bar is already dry."
Some colleagues used far more frightening phrases to describe the difficult situation of the Prime Minister.
An anonymous ally of former Brexit secretary David Davis, whom some see as an interim leader if Ms. May falls, said he was entering "the killing area."
Others spoke of "murder in the air" and the moment arrived "when the knife warms up, gets stuck in his forehead and writhes, he will die soon".
Brexit: Dominic Raab urged Tory MPs to join and keep their nerve
One Brexiteer warned Ms. May that she must "bring her own ribbon" if she comes to address the rank and file the parliamentarians at her 1922 Committee meeting on Wednesday.
This language was condemned by some conservative parliamentarians, including critics of Ms. May.
Tory deputy Andrew Rosindell said: "I do not like that language and we should support the prime minister, but she has to understand that we can not continue to compromise and look like we are running away."
A tall Tory warned: "I suspect that the bad language will encourage the vote of payroll to gather around him."
However, there is uncertainty about who should replace Ms. May and how quickly it could happen at a critical moment in the Brexit negotiations, with only a few months until next March 29.
Brexit: Iain Duncan Smith urged British negotiators to show "self-confidence and spine"
Former Brexiteer cabinet minister Theresa Villiers told the BBC that some of the terms were "disturbing and really useless" and that now was not the time for a contest.
Tory's former minister, Robert Halfon, said a new leader would make no difference if the party had the wrong values, and the harsh language was not "the way to change things." It simply confirms what many people think of us, that we are all potentially by ourselves and not by the workers' side ".
The Brexit minister, Suella Braverman, refused to criticize the violent language about the prime minister and refused three times to tell BBC Radio 5 Live that she would support Ms. May in a secret vote of confidence.
But she said she did not expect such a vote, that she supported the PM "unequivocally" and that the Tories should come together and remember that the greatest threat to Britain is a government of Jeremy Corbyn.
The secretary of Brexit, Dominic Raab, urged the restless conservative parliamentarians to join and wait for the agreement with Brussels that, he said, was almost finished before taking any action.
He told Andrew Marr of BBC One that he understood the "frustration and nervousness" of people at this critical stage, but he urged people to "stay calm."
"Now is the time to play for the team, that's the way we get the best deal from the EU and I also think that's what the country expects from us."
The potential leader, Mr. Davis, used an article in the newspaper The Mail on Sunday to urge the UK to be tougher on the EU and clarify what the bloc might lose in a Brexit without agreement.
By saying that Mrs. May had infuriated both Leaves and the ardent remnants, Davis warned that he could squander the Brexit's "golden opportunity."
Former Cabinet Minister Iain Duncan Smith in The Sunday Sun urged British Brexit negotiators to show "self-confidence and a backbone," as Margaret Thatcher would advise.