Theresa May is addressing a packed meeting of backbench Tories amid calls for her to name her departure date.
The prime minister will make another bid to win over opponents of her EU withdrawal agreement in a speech to the 1922 committee.
Some Tory MPs want her to name a date to stand down as a price for their support for her deal.
It comes as MPs seize control of the Commons agenda to hold votes on alternatives to the deal.
Mrs May’s critics don’t want her to be still in charge for the next phase of Brexit talks, when the two sides hammer out what kind of trading relationship they will have – if her deal is passed by Parliament.
The PM has said she wants to bring the deal back to the Commons this week, after it was previously rejected twice, by large margins.
Conservative MP Tim Loughton told the BBC’s Politics Live he believed “we’re at the end game” of Theresa May’s tenure as prime minister.
He said it was “inevitable” that she would have to resign, but called it a “great tragedy” that her premiership would come to an end in the manner he expects it to.
The BBC’s Iain Watson said Mrs May received a “muted” reception from Conservative MPs as she arrived at the meeting.
Speaker calls for changes
Commons Speaker John Bercow ruled last week that the government could not return for a third attempt, unless there had been “substantial” changes to the proposals.
And he warned ministers earlier that they should “not seek to circumvent my ruling” by introducing procedures that could reverse his judgement.
But a Downing Street spokesman said there had been a “significant development” at the summit in Brussels last week, after Mrs May agreed “extra reassurances” over the Irish backstop with the EU, and the date of exit had changed.
Many Tory Brexiteers are looking to the Democratic Unionist Party, who have led opposition to the PM’s deal, before deciding whether to get behind it.
Jacob Rees-Mogg, the chairman of the European Research Group of Tory Brexiteers, told the BBC: “I think that we have got to the point where legally leaving is better than not leaving at all.
“Half a loaf is better than no bread.”
He said his only condition for supporting the deal was that Mrs May wins round the DUP.
“I won’t abandon the DUP because I think they are the guardians of the union of the United Kingdom,” he said.