Prime Minister Theresa May has said for months that she would invoke Article 50 of the EU's key treaty, the trigger for two years of exit negotiations, by March 31.
Brexit minister David Davis said it was in "everybody's interests that we get a good outcome", but said the government was "planning for the contingency, all the various outcomes". Lawmakers on Monday are slated to vote on changes sought by the House of Lords - but panned by the government.
The Prime Minister confirmed she expected royal assent to be granted "in the coming days" to the Bill granting her the power to begin negotiations with the EU.
May will officially have the authority to trigger Article 50.
The government's plans have also been disrupted by Scottish first minister Nicola Sturgeon's decision to call for a second referendum on Scottish independence while negotiations are underway.
The House of Lords voted not to insist on its original amendments giving protections to European Union citizens in a post-Brexit Britain and called for a "meaningful vote" on any divorce deal.
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But Mr Davis succeeded in warding off a potential rebellion in the lower chamber, the House of Commons, where Ms May only has a slim majority, from a handful of pro-EU Conservatives who say parliament should be able to prevent the government walking away from negotiations and leaving without a deal.
The House of Commons rejected amendments by the House of Lords, calling on the government to protect the status of European Union nationals within three months of the start of Brexit talks, by 335 votes to 287. In the last one, in 2014, Scotland voted 55% to 45% to remain in the United Kingdom.
But beyond saying she will begin the formal process later this month, the Premier has yet to answer the question of exactly when, and end nine months of guesswork as to how her government will approach the uncharted territory of leaving the EU.
"All the signs are that we have a complacent government", Corbyn added. "I don't think the consequences of no deal are by any means as apocalyptic as some people like to pretend", he said.
The Labour Party's Brexit spokesman, Keir Starmer, told Sky News that he expected it to happen on Wednesday or Thursday.
The passing of the legislation is overshadowed by the possibility of Scotland's exit from the United Kingdom as the country called on for the referendum in order not to leave the EU.
The Brexit Secretary told Parliament earlier this week that "we can not have...any suggestion that the votes in either House will overturn the result of the referendum" and dismissed "any prospect that we might actually decide to remain in the European Union".