Britain is due to pull out of the European Union in less than three weeks, on March 29, but the government has not been able to win parliamentary approval for its agreement with the bloc on withdrawal terms and future relations.
Parliament rejected May's deal by 230 votes on January 15, prompting the British leader to return to Brussels in search of changes to address the so-called Irish backstop - an insurance policy created to prevent the return of a hard border between Ireland and Northern Ireland.
Foreign Secretary Jeremy Hunt has issued a stark warning to Tory MPs that they risk losing Brexit altogether if they fail to back Theresa May's deal in the crunch Commons vote on Tuesday.
British parliament will vote whether the country needs more time for an orderly exit. She has already said she will stand down before the next election, in 2022, but there is already pressure from inside her own Conservative Party for her to quit within the next few weeks if she can not deliver Brexit on time. "Whether they listen or not is another matter", a senior member from the Conservative Party told the newspaper.
Many British lawmakers object to the policy on the grounds that it could leave Britain subject to European Union rules indefinitely and cleave Northern Ireland away from the rest of the country.
Leadsom appealed to Labour, Conservative and Scottish Nationalist Party members to back the deal and defer seeking changes until they debate legislation in the weeks ahead.
May's deal was struck during more than a year of tough negotiations, and covers Britain's financial settlement, expatriate rights, the Irish border and plans for a transition period.
Late Monday, Cabinet Office Minister David Lidington announced in the House of Commons that the two sides had agreed on "legally binding changes" to a portion of the deal relating to the Irish border.
Zinedine Zidane confirmed as new Real Madrid manager
French professional football coach and former player Zinedine Zidane has returned to Real Madrid as manager, the Spanish football club said in a statement .
The prime minister has warned that a defeat risks scuttling her blueprint for Brexit and replacing it with a scaled-down plan, potentially keeping the United Kingdom inside the EU's single market and customs union.
The shadow Brexit secretary, Keir Starmer, immediately cast doubt on whether the changes would actually be legally binding, saying: "It sounds again that nothing has changed".
A plane was reported to be on standby at RAF Northolt to fly her to Brussels to clinch an agreement if there was any sign of a deal emerging from talks over the weekend between officials.
Fellow MP Jacob Rees-Mogg, an influential Brexit supporter, wrote in the Express: "Leaving without an agreement is nothing to be frightened about".
The government's motion, due to be voted on by MPs on Tuesday, refers to a unilateral declaration setting out the sovereign action the United Kingdom would take to ensure the backstop would only be applied temporarily.
The EU has said it is now up to MPs to decide the next steps for Brexit and it remains "committed" to agreeing a deal.
Any delay would have to be approved by the leaders of the other 27 nations, who are next meeting at a Brussels summit on March 21-22 - a week before Brexit day.
The talks are still continuing on Monday, only a day before the withdrawal agreement, which May said the backstop would be replaced by alternative arrangements, will see a second vote in the parliament on Tuesday.