After talks with opposition Labour leader Jeremy Corbyn on Tuesday evening, May announced that MPs would vote on legislation to implement the Brexit deal in the week starting June 3.
But Labour warned it had not yet agreed to support the bill, while May’s Northern Irish allies said that unless the EU agreement changed, they would not back it.
May struck a deal on Britain’s exit terms with the European Union in November, but it has been rejected by the House of Commons three times.
Unwilling to end more than four decades of EU membership without new arrangements in place, she has delayed Brexit twice, most recently to October 31.
Setting a date for the next parliament vote without an agreement with Labour is a gamble — if she loses, May cannot hold another in the current parliamentary session.
But the Brexit delays have caused huge anger among her Conservative MPs as well as voters, and the party is braced for an electoral drubbing at European polls next week.
May is also under intense pressure to fulfil her promise to MPs to deliver Brexit and then stand aside for a new leader.
On Thursday, she will meet senior Conservatives who have demanded a detailed timetable for her departure.
Her ministers — many of whom are already jockeying to replace her — agreed this week that any Brexit deal must be passed before parliament’s summer holiday at the end of July.
Britain could then leave the EU on July 31.