The deal reflects Switzerland's "mind the gap" strategy of ensuring seamless trade ties with Britain, regardless of whether London is able to strike and approve a formal exit agreement with Brussels by March 29, the date it is scheduled to leave.
Communities Secretary James Brokenshire said Sunday that parliament would get another chance to pass judgment on May's Brexit plan "by no later than February 27".
Labour leader Jeremy Corbyn has written to the Prime Minister setting out five demands that would have to be met for his MPs to support a deal, including a permanent customs union and close alignment with the single market.
Should the parliament give May more time on Thursday, it would mark the second extension since her Brexit deal was defeated by MPs in January.
Mrs May survived a confidence motion in her government tabled by Mr Corbyn, which could have led to an election, after her Brexit deal was overwhelmingly rejected by MPs last month.
Asked by Sky News if she could stay in office if that became government policy, Tuss said: "I absolutely do not think that should be our policy".
Labour's Brexit vote brigade An amendment, to be tabled by the Labour front bench and pushed by the shadow Brexit secretary Sir Keir Starmer may struggle if it does not attract cross-party support or get picked up in another guise by a Conservative backbencher.
The government has not ruled out supporting this - and has promised a formal response to it and further talks with Labour - but they say it would prevent the United Kingdom from making its own trade deals after Brexit. "That isn't right in terms of the respect for parliament", said Starmer.
The impasse risks a chaotic "no deal" departure for Britain, which could be painful for businesses and ordinary people on both sides of the Channel.
'It's this blinkered approach that's got us to where we are, with her never wanting to see where the real majority is in Parliament, ' Sir Keir said. The prime minister is now in talks with Brussels to seek these changes to the backstop.
Christine Lagarde spoke at the World Government Summit in Dubai, where she didn't hesitate to criticize Britain's upcoming departure from the European Union, known as Brexit.
A number of government ministers will also be meeting their counterparts across the continent this week, in order to underline Mrs May's determination to achieve a deal.
She also said she hoped to have further discussions with Labour over the "alternative arrangements" to the backstop to the Northern Irish border which she is seeking to secure with European Union leaders.