She will urge MPs to "hold our nerve" to get the changes to the Brexit deal.
As companies and governments across Europe step up preparations for the turmoil of a no-deal exit, diplomats and officials said the United Kingdom now faces three main options: a no-deal exit, a last-minute deal or a delay to Brexit.
In the case of a no-deal Brexit, May said the government would prioritise medicines being brought into the country.
Responding to May, Labour leader Jeremy Corbyn said Britain was facing the biggest crisis in its history, accusing her of playing for time to win backing for her Brexit deal by running down the clock towards the Brexit day on March 29.
That could open the prospect of an European Union summit scheduled for 21 March being the final opportunity for the heads of government to finalise a deal before the United Kingdom formally leaves the European Union on 29 March.
May said she will present an amendable Brexit motion for debate in the House of Commons on Thursday, giving politicians a chance to challenge her Brexit process and put forward alternatives. The EU and Ireland have insisted the backstop must remain in order to uphold the provisions of the 1998 Good Friday Agreement which ended decades of sectarian violence and eliminated border controls between Ireland and Northern Ireland. Mr. Barnier has said the European Union was willing to consider changes to the "political declaration" a 26-page framework for future negotiations on an EU-U.K. trade deal, but many Tory MPs have said that won't go far enough. "Extension is possible but if they don't vote for the deal then the extension is a long one..."
As expected, the European Commission President Jean-Claude Juncker said the EU would not reopen the withdrawal agreement agreed between the British government and Brussels.
"This time that remains is extremely short", he added.
Leadsom, responsible for bringing government business through parliament, said the talks were "pretty crucial but delicate negotiations with the European Union to try to make sure that we can sort out the problem with an unlimited backstop".
Media captionConfused by Brexit jargon?
MPs last month overwhelmingly rejected the deal struck between May and Brussels and the British premier has since been attempting to secure changes that would satisfy parliament's lower House of Commons. "She is playing for time, and playing with people's jobs, our economic security and the future of our industries". "It's a high-wire act and - gulp - might lead to a no-deal".
UK Prime Minister Theresa May.
A video grab from footage broadcast by the U.K. Parliament's Parliamentary Recording Unit shows British Prime Minister Theresa May in the House of Commons, in London, on February 12, 2019.
"The talks are at a crucial stage", Ms.
That is how May intends Brexit to unfold, her chief negotiator, Oliver Robbins, is reported to have said.
The 21-day period is usually meant to give parliament time to study an agreement but it will already have had plenty of time to do so as the deal was reached past year, May said.
A similar amendment that set a deal deadline of 26 February and suggested the possibility of extending Article 50 was tabled by Ms Cooper and narrowly defeated in the Commons in January.