May's hopes of delivering an on-time Brexit were also undermined by an ITV news report which cited Britain's lead negotiator Olly Robbins as being overheard in a Brussels bar saying: "In the end, they (the EU) will probably just give us an extension".
Asked in an interview with the Press Association if she would resign if the PM adopted Labour's proposals for a customs union with the EU after Brexit, the Commons Leader said: "I've read the Prime Minister's letter and I don't think she's softening her stance at all". Only six of 40 European Union trade deals are on course to be rolled over in time for Brexit, The Sun newspaper reports.
The focus of numerous pro-Brexit lawmakers is the motion the government will put forward on Thursday, which some suggest takes a no deal scenario off the table.
Ms Sturgeon said it was "reckless and negligent" for the United Kingdom government to refuse to rule out no-deal, adding: "But we appear to be dealing with a United Kingdom government that's prepared to act recklessly and negligently".
"By getting the changes we need to the backstop; by protecting and enhancing workers' rights and environmental protections; and by enhancing the role of parliament in the next phase of negotiations I believe we can reach a deal that this House can support", May said.
Other MPs supporting the move include the senior Labour MP Hilary Benn, Tory former attorney general Dominic Grieve and the Liberal Democrat Norman Lamb.
None are expected to win enough support to pass, with lawmakers who are seeking to force the government to delay Brexit saying they will wait until the next round of votes May has promised on February 27 to make their move.
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In a statement updating the Commons on progress in talks, Mrs May acknowledged she would need "some time" to seek legally-binding changes from the European Union to the controversial backstop for the Irish border.
The United Kingdom is on course to leave the European Union on March 29 without a deal unless May can persuade the bloc to amend the divorce deal she agreed a year ago and get it approved by British lawmakers.
And a cross-party initiative backed by Conservative Anna Soubry and Labour's Chuka Umunna demands that the Government publish its most recent official briefing on the implications of a no-deal Brexit for business and trade.
With 45 days to go however, Mr Grieve warned time was running perilously short under the terms of the Constitutional Reform and Governance Act which requires 21 sitting days before the ratification of any global treaty.
Speaking after a meeting of the Scottish cabinet in Glasgow, Ms Sturgeon told BBC Scotland that Mrs May was attempting to "run down the clock" in an attempt to "blackmail" MPs into backing her deal "at the very, very last minute".
But Mrs May responded: "In this instance MPs will already have debated and approved the agreement as part of the meaningful vote".