The prime minister is facing calls to resign amid a backlash against her Brexit plan from Conservative MPs.
Several cabinet ministers have told the BBC that she cannot stay, with one saying it is “the end of the line”.
Others, though, insist maybe Theresa ought to push on with her plan to put her Withdrawal Agreement Bill to a vote.
May’s own Members of Parliaments have been unhappy with the concessions she has set out in the bill, but she has called for “compromise on all sides”.
She told MPs that the bill which includes the promise of a vote on a further referendum and different customs options – would be published on Friday.
The PM has pledged to set a timetable for a new leader to take over after MPs vote on her compromise Brexit plan in the week beginning 3 June.
However, some MPs are again seeking to change party rules, so they can vote to oust her at a meeting of backbench MPs.