The United Kingdom is on course to leave the European Union on March 29 without a deal unless May can convince the bloc to amend the divorce deal she agreed last year and get it approved by British lawmakers, Reuters reported.
"The talks are at a crucial stage," May told Parliament. "We now all need to hold our nerve to get the changes this House requires and deliver Brexit on time."
The leader of the opposition Labour Party Jeremy Corbyn accused her of running down the clock with sham negotiations to pressure Parliament into backing her deal.
British lawmakers rejected May's withdrawal deal last month, with the major sticking point being the Irish backstop.
"By getting the changes we need to the backstop; by protecting and enhancing workers' rights and environmental protections; and by enhancing the role of Parliament in the next phase of negotiations I believe we can reach a deal that this House can support," May said.
The EU's Brexit negotiator Michel Barnier said on Monday the bloc would agree to tweak the political declaration on EU-UK ties after Brexit that forms part of the package, to reflect a plan for a closer future relationship that could remove the need for the backstop.
May is pursuing three options in talks with Brussels: negotiating a way for Britain to leave the backstop without needing EU agreement, agreeing a time limit to the backstop, or finding an alternative arrangement that replaces it altogether.
Parliament is to hold a debate on Brexit on Feb. 14 but with just 45 days until Britain leaves the bloc it is not expected to change the course of the exit process, and no date has been set for another vote to approve or reject May's deal.
May said if she had not yet reached a deal in Brussels, she would deliver another progress report on Feb. 26 and provide another chance for Parliament to express its opinion on her approach the following day.
May said she was prepared to speed up other parts of the ratification process of the Brexit deal if time gets too tight to pass legislation before exit day – a move some interpreted as a sign she was willing to keep negotiating until the last moment.