May, who narrowly defeated a no-confidence vote in her Conservative government triggered by Corbyn this week, said it was "not within the government's power to rule out no-deal" because by law Britain will leave the European Union without an agreement on March 29 unless Parliament approves a deal before then.
"No-deal will only be taken off the table by either revoking Article 50, which turns back the results of the referendum - the government will not do that - or by having a deal, and that is what we are trying to work out", May said.
May sat stony-faced as Labour deputy leader Tom Watson savagely said she lacked "the empathy, the ability and, most crucially, the policy to lead this country any longer".
Dr Fox said one way to break the deadlock could be an agreement with the Irish Government on an "alternative mechanism" to the backstop, meant to ensure there is no hard border with Northern Ireland, which is a key stumbling block for many MPs.
"I will then take the conclusions of those discussions back to the EU", May said.
May spoke to Dutch Prime Minister Mark Rutte and German Chancellor Angela Merkel on Thursday, and to European Union leaders Jean-Claude Juncker and Donald Tusk by telephone Friday to discuss where to go next on Brexit.
Senior sources within the European Union say her unchanged stance, and the fact she didn't make any new demands, was "greeted with incredulity" following a call with German Chancellor Angela Merkel.
After May's motion is published, lawmakers will be able to propose amendments to it, setting out alternatives to her deal. "We actually agree that no matter what, there should be an agreement that ensures that there's no hard border between the United Kingdom and Ireland", he said.
She said Monday that a new referendum, less than three years after voters opted for Brexit, would "damage social cohesion by undermining faith in our democracy".
Shutdown Projected to Cause $3 Billion Permanent Hit to Economy
Though federal employees are expected to receive back pay, contracted employees likely will not. Furloughed workers wait in line to receive food and supplies in Washington , on January 22.
Steven Fielding, a professor of political history at the University of Nottingham, said Brexit has paralyzed the U.K.'s parliamentary system. An open border with Ireland is widely seen as crucial to maintaining this peace.
Mr Grieve said he wanted to use the debating time controlled by backbenchers to enable the House to indicate what sort of Brexit it would support.
Chief EU Brexit negotiator Michel Barnier said that while the EU wouldn't amend the legally binding withdrawal agreement, it was ready to adjust the political declaration - a non-binding statement on future relations that forms the second part of the divorce deal.
Parliament will vote on January 29 on different options put forward by lawmakers, potentially opening up a way out of the stalemate.
He drew the loudest cheer, however, when he said Labour stood by the commitment made at the party conference previous year in Liverpool that if it was unable to force a general election all options must remain on the table - including another referendum.
She told the paper: "No deal is not the desired outcome, but it would be incompetent for any responsible government to rule it out, and there are very good reasons for that".
There are few signs she plans to make radical changes.
Jacob Rees-Mogg, chairman of the European Research Group of anti-EU lawmakers in May's party, said Britain was most likely to leave without a deal.
May's spokesman, James Slack, said that May's talks with opposition lawmakers were "genuine", and that a "significant number" had expressed concerns about the backstop. On the day of the referendum in 2016, it was trading at $1.50.