A major sticking point to her withdrawal deal is an agreement to ensure no hard border returns between Northern Ireland and the Republic of Ireland. Some Brexiteers feel that "backstop" could be used by Brussels as a means to keep Britain within the EU while the Northern Irish Democratic Unionist Party (DUP) is nervous it would lead to Northern Ireland being treated differently from the rest of the U.K.
In a statement to the lower house of Parliament on Monday afternoon, May said she would now discuss with the DUP on how to allay fears among the people of Northern Ireland before returning to negotiate further with Brussels.
However, May said the prospect of a second Brexit referendum did not enjoy majority support and also rejected the growing calls for her to rule out a "no-deal" Brexit as a possibility.
"The right way for this house to rule out 'no deal' is for this house to approve a deal with the European Union," she said.
In what appeared to be some small concession to opponents, May said her government would also guarantee that workers' and environmental rights would not be eroded post-Brexit and that a £65 ($84) fee for EU nationals applying for settled status would now be abolished.
May said she would continue to hold further meetings on Brexit next week and hoped that opposition leader Jeremy Corbyn would hold talks with her. Corbyn's response to May's statement was to accuse her of failing to realize the extent of her defeat last week and that her cross-party talks have been a "sham."
Prior to the statement, sterling sat at 1.2870 versus the dollar and rose to $1.2890 as she spoke.
Parliament will now debate Monday's statement from the U.K. leader before a vote on the motion is taken on Tuesday January 29.
In what is being described as an attempt to pull the U.K. toward a "softer" Brexit, several amendments are expected to be attached to May's plan. The amendments are also being characterized as an attempt by some lawmakers to take control of the Brexit process away from the government.
Two amendments are expected to be tabled by Conservative Party lawmaker Dominic Grieve which will include a request for a second referendum and putting a pause on Article 50. Article 50 is the two-year countdown to Brexit that May activated in March 2017. Any extension would require the permission of the 27 remaining EU countries.
Another amendment, jointly sponsored by Labour's Yvette Cooper and the Conservative Party's Nick Boles, seeks to delay Article 50 until the end of 2019.
Labour lawmaker Frank Field is also reported to be considering amendment which would allow MPs to vote on a raft of different Brexit scenarios.
As things stand, the legal default is that the United Kingdom will leave the EU in 68 days on March 29, 2019 with no agreed deal on trade, laws or travel.
That scenario would particularly alarm business leaders and trade union representatives who May is due to meet with later this week.