With the European Union saying so far that they are not willing to reopen talks on the Withdrawal Agreement, other lawmakers are likely to propose alternatives to May's deal to gauge support for them and persuade the prime minister to change course by seeking closer European Union ties or holding a second referendum.
She has said she wants to bring a revised deal back to parliament for a vote "as soon as possible" but has not yet set a date for doing so. We've now got a response from the prime minister.
Labour's Brexit policy chief Keir Starmer told the Sunday Times newspaper that his party would seek to use the debate in parliament this week to prevent May from waiting until the last minute to come back with a deal, and compel her to present a fresh accord for lawmakers to consider before February 26.
Yvette Cooper and Nick Boles, two senior backbenchers whose anti-no-deal amendment failed to gain majority support last month, have not yet made a final decision about whether to table a reworked version or wait until 27 February, the Guardian understands.
The government has signed a trade deal with Switzerland, heralded as the most significant such agreement in the run-up to Brexit.
The British government is seeking to win more time to secure European Union concessions on Brexit that could pass parliament and avert a chaotic split from the bloc on March 29.
"We shouldn't be put in a position where the clock is run down and the prime minister says it's either my deal or even worse", Labour's Brexit pointman Keir Starmer told The Sunday Times.
Michel Barnier said Monday that he still doesn't see a "clear and stable majority" of support among British lawmakers for any Brexit plan, especially one that would also respect the EU's demands.
At a briefing in Parliament on Friday, Vandendriessche said, "We deplore Tusk's statement which also demonstrates the unwillingness of certain European Union officials to work for an agreement and [it] is profoundly distasteful". In the event of a no-deal Brexit, these would need to be completed by 29 March, an ambition that many in British business now believe to be nearly impossible.
"It seems to me we're now at the point where we can have meaningful talks to get a deal between the main political party leaders", he said.
According to papers to be discussed by the Cabinet's Brexit sub-committee on Monday, the European Commission has told members states to "refrain from bilateral agreements or discussions with the United Kingdom, which would undermine EU unity". He says May's agreement can achieve "a great deal of what Jeremy Corbyn is interested in without taking away that option of having other trade deals".