But speaking on the BBC's Andrew Marr Show on Sunday, the Scottish First Minister said Theresa May had not revealed what her next plan for Brexit was - meaning extending Article 50 was "now pressing and urgent".
The parliamentary notion covers both a scenario under which Prime Minister Theresa May breaks the deadlock at home and manages to get the divorce deal she had negotiated with the European Union ratified in the UK Parliament, as well as a no-deal Brexit.
Parliament will vote on proposals made by lawmakers including a delay to Brexit and going back to the European Union to demand changes to the Northern Irish backstop.
"Even if the prime minister's deal was to somehow achieve a majority in this House next month, there is no chance that the necessary legislation - primary legislation and an extensive category of second legislation, I believe there are over 600 statutory instruments - could clear this place between now and 29 March", he said.
The diplomat said some of the problems caused by opposition to the so-called "Irish backstop" - created to keep open the EU-UK land border on the island of Ireland - by changing some of its demands on post-Brexit trade. Other proposals including the Conservative party amendments seeking removal of the controversial Northern Ireland backstop even with the European Union standing clearly against such move. May said her intention was to ask Brussels for more concessions on the Irish border backstop in a bid to secure backing of fellow Conservative lawmakers and their allies, the Democratic Unionist Party (DUP), who have been critical of the backstop.
MPs in her own party want her to demand a last-minute change to the withdrawal deal to remove the backstop, which they fear could end up trapping the United Kingdom in a permanent customs union with the EU.
Dismissing calls for changes to the backstop as "like Groundhog Day", she insisted the EU27 were unanimous in opposing any time limit.More news: Taco Bell evacuated, WWII grenade safely removed
She said that she would seek "legally binding" agreements for any new deal but admitted negotiations would not be easy.
At the weekend, Ireland's foreign minister, Simon Coveney, stated baldly the backstop simply "isn't going to change".
"There can be no change to the backstop".
The German diplomat, who has been the deputy to Michel Barnier during the Brexit negotiations, said Brussels had a "margin" for movement on the political declaration about the future trade deal.
It was far from certain the amendment would win support from a majority in the House of Commons.
May's approach drew praise from "hard-Brexit"-backing lawmakers who have often opposed her".
But Green Party legislator Caroline Lucas accused May of chasing "heated-up fantasies that have already been rejected by the European Union".More news: Postal Service suspends delivery January 30, 2019
Speaker of the House of Commons John Bercow selected seven proposals for votes on Tuesday (local time), including the border change supported by Mrs May and several measures that seek to rule out a "no-deal" Brexit.
Increasing numbers of government ministers have warned they will not accept the prospect of Britain leaving without a deal on Mar 29, immediately severing all ties with its largest trading partner and threatening economic chaos.
The prime minister's original Brexit proposals were thrashed by the parliament on January 15, with the government losing by record 230 votes.
The Liberal Democrats' amendment would, similarly, force the government to rule out a no-deal exit, but it would also instruct the Cabinet to set up another Brexit referendum.
Today's votes will not mark the end of Britain's turmoil over Brexit.
"This is not a Brussels day, this is a London day", said European Commission spokesman Margaritis Schinas.
This was one of the seven amendments to the Brexit bill being voted on in parliament.More news: Russian hackers ‘stole evidence from Mueller probe into Trump’