With Britain's departure from the bloc just 45 days away, Mrs May tried to avert a rebellion Thursday when Parliament votes again on Brexit by promising another series of votes two weeks later.
EU Brexit negotiator Michel Barnier said on Monday the bloc would agree to tweak the political declaration on EU-U.K. ties after Brexit that forms part of the package, to reflect a plan for a closer future relationship that could remove the need for the backstop.
Parliament is to hold a debate on Brexit on February 14, but with just 45 days until Britain leaves the bloc it is not expected to change the course of the exit process, and no date has been set for another vote to approve or reject May's deal. The final vote on whether Britain leaves the European Union on March 29 with a deal would be pushed back into March.
"It appears that the Prime Minister has just one real tactic: to run down the clock, hoping that members of this House can be blackmailed into supporting a deeply flawed deal", Labour Leader Jeremy Corbyn told MPs. "We now all need to hold our nerve to get the changes this house requires and deliver Brexit on time", May told lawmakers.
Robbins suggested the strategy would be to tell the Commons in the final week of March that if an amended version of the government's deal wasn't passed, talks would have to be extended, potentially for a long time, ITV reported Tuesday.
The opposition was having none of this.
After it has voted to support her deal, parliament must also pass a law - the Withdrawal Agreement Bill - formally ratifying the agreement.
She said the plan must change if it is to win the support of MPs who urged her to seek "alternative arrangements" to the backstop when rejecting the deal last month.
The UK and EU made a commitment to avoid physical barriers or checks on the border if no UK-EU trade deal is agreed before the Brexit transition period ends. The free flow of people and goods across the frontier has been an important measure upholding Northern Ireland's peace deal.
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But EU leaders insist the legally binding withdrawal agreement can't be changed.
"Both sides want a Brexit deal that supports ongoing friendship between UK/EU/France so patience and goodwill on backstop now the critical ingredient", he tweeted.
Opposition MPs accused her of deliberately dragging out the process so that MPs will be forced to either accept her deal or risk the country leaving without an agreement.
Brexiteer MPs in her Conservative Party are particularly unhappy with the so-called backstop provision meant to keep the border with Ireland free-flowing.
The political impasse leaves Britain lurching toward a chaotic no-deal departure that could be costly for businesses and ordinary people in both the United Kingdom and the EU.
May "is playing for time and playing with people's jobs, our economic security and the future of our industry", said Corbyn.
Earlier in the day, the Leader of the House of Commons Andrea Leadsom refused to rule out delaying the British parliamentary vote until as late as the week prior to Brexit, following an European Union summit scheduled for March 21.
"It is a negotiation".