One of the most problematic areas of the divorce deal is the so-called backstop on the Irish border - a legal guarantee that the frontier would remain free-flowing if Britain and the European Union can not agree a long-term free trade pact.
Westminster can not be allowed to hijack Brexit, says the United Kingdom's International Trade Secretary Liam Fox, in a warning to MPs who want to take more control over the country's departure from the European Union.
"Parliament has not got the right to hijack the Brexit process because Parliament said to the people of this country "We make a contract with you, you will make the decision and we will honour it"".
Cabinet sources have told Sky News that Mrs May made clear she was ditching efforts to seek a cross-party compromise, because the level of support expected from Labour MPs was not deemed strong enough to pass the Withdrawal Agreement and the subsequent Brexit legislation required before the United Kingdom leaves the EU.
Time is running out for Brexit, the country's biggest shift in foreign and trade policy in more than 40 years, but so far there is little that unites a divided Parliament beyond its rejection of Mrs May's deal that envisages close economic ties with the EU.
Starmer said there was a roadblock in the way of a solution to the Brexit crisis, "and that roadblock is the Prime Minister".
Dr. Fox also took to the airwaves on Sunday to drum up support for the embattled May, accusing a "remain Parliament" of stealing Brexit from a "leave population".
Britain will leave the European Union on March 29 without a deal unless MPs can force a delay or get their act together in time and come up with an alternative plan that Brussels is also happy with. Many economists expect Britain to plunge into recession if there is a "no-deal" Brexit.
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"We're ready to talk to the government and others in parliament about a sensible alternative plan, but not while Theresa May is wasting 171,000 pounds ($220,000) an hour of taxpayers' money on risky and unnecessary no-deal brinkmanship", he said in a statement.
Instead, Mrs May is expected to set out plans to try and "remove the Irish backstop" in an effort to win around the DUP, whose 10 MPs she relies on for support in parliament, and some of the 118 Conservatives who opposed her deal last week.
He said it is up to Jeremy Corbyn to seize the initiative on Brexit and said he was "frustrated" with the Labour leader's approach.
A Labour and Co-op MP has called on the Labour Party to adopt the second referendum as official party policy as a way of breaking through an "impasse" over Brexit.
He said: "We are in a position where we are facing a possible no deal".
Fox's media offensive comes as two groups of backbenchers make maneuvers to wrestle control from the government over the Brexit process in order to prevent a no-deal scenario by pausing Article 50.
"We've arrived at phase three, we need to think about what the options are".
He said public anger could trigger "a political tsunami".