Mrs May urged lawmakers earlier this evening to take "a second look" at her deal to leave the European Union, warning them that voting it down could open the way for the break up of the United Kingdom.
"I say to members on all sides of this house, whatever you may have previously concluded, over these next 24 hours, give this deal a second look," she told parliament.
May is now partly relying on assurances from the EU on the backstop to persuade more MPs to support her plan.
European leaders Jean-Claude Juncker and Donald Tusk have issued a letter to the British Government, which was made public this morning.
Says EU is committed to speedy work on trade deal by December 2020 to avoid triggering Irish backstop
Says, even if triggered, backstop would only be temporary, until better agreement found
Says EU council decisions have legal value
EU letter to May says withdrawal agreement and political declaration on future are linked under Treaty Article 50
Says the letter does not change anything in the Withdrawal Agreement
Also says EU 'does not wish to see the backstop enter into force'
Winding up the debate for the British government this evening, Lord Keen of Elie urged MPs to back Mrs May's deal, warning the alternatives were worse and Parliament must respect the result of the referendum.
Lord Keen said a second referendum would be seen by some as a "constitutional outrage", and insisted the 2016 referendum was a "people's vote".
For Labour, Baroness Hayter of Kentish Town condemned the political declaration as a "dismally inadequate" means of ensuring the UK's future relationship with the EU.
Lady Hayter said the Prime Minister had wasted two years negotiating with her own party and put "blinkered Brexiteers" in charge, who rejected all evidence at variance with their "ideological obsession".
Labour's alternative was a customs union, she insisted.
Liberal Democrat Baroness Ludford said the country had been "held to ransom" by squabbling in the Conservative party and hoped that in a people's vote the British people would choose to remain in the EU.
"Nothing can be as good as EU membership," she told a packed chamber after more than 130 peers had taken part in the debate.
Earlier, the deal was branded a "terrible shambles" by former chairman of the Conservative Party Lord Patten of Barnes.
Lord Patten warned that arguments over the EU were set to "pollute British politics" for a long time to come, even if the deal was agreed to in tomorrow's crunch Commons vote.
He also warned of "collateral damage" to both the Tories and the country over Brexit and urged MPs to limit the damage in a way that did not make Britain poorer or less influential in the world.Earlier this evening, the UK Prime Minister issued a last-ditch appeal to Tory MPs to back her Brexit plan, warning that defeat in Tuesday's crunch vote could hand the keys of No 10 to Jeremy Corbyn.
With the Government braced for a crushing defeat, the Prime Minister told a private meeting of Conservatives at Westminster they had a duty to deliver on the EU referendum vote.
It followed warnings that pro-Remain MPs are preparing to seize control of the Commons timetable in a bid to thwart Brexit altogether.
In the Commons, Mrs May warned any move by MPs to prevent the UK leaving the EU would be a "subversion of democracy".