The defeat on Tuesday clears the way for further votes in Parliament on Wednesday that could clear the way for a "no-deal" Brexit, which would end decades of European integration on March 29, or allow MPs to request a delay.
Speaker of the House John Bercow said on Wednesday that the government motion will be amendable, meaning MPs may try to gain a majority for the length of the delay or type of Brexit as part of the extension.
The motion was deliberately vague, essentially saying that the government does not wish to actively pursue no-deal Brexit as official policy, yet acknowledged that no deal is the default option, should nothing be agreed before March 29.
Prime Minister Theresa May leaves after the weekly cabinet meeting at 10 Downing Street on Tuesday.
The European Research Group said the verdict of its "Star Chamber" set up to analyse the assurances was that they did not deliver legally binding changes to the Brexit deal or the Irish backstop and did not provide an exit mechanism over which Britain had control.
But the prospects of getting her deal through were effectively crushed on Tuesday morning when Attorney General Geoffrey Cox failed to convince critics that Mrs May had secured enough changes to the plan that was crushed by 230 votes in January. "I do not think that would be the right outcome", the Prime Minister told lawmakers.
"It is increasingly clear that the only way forward is to put this question back to the people, so they can have the final say on staying in the European Union or leaving on Theresa May's terms". "Now is the time to come together, to back this improved Brexit deal, and to deliver on the instruction of the British people".
Some MPs have already proposed extending Article 50 until the end of this year, while it has been reported the European Union could even seek a delay to Brexit until 2021.
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In a surprise move, the Commons voted 312 to 308 - a majority of four - in favour of the proposal tabled by former Conservative chairman Dame Caroline Spelman. The discussion on Article 50 is done and dusted.
It went further than the government's position of keeping the threat of a "no-deal" Brexit on the negotiating table - a stance many in her party said was essential to push Brussels to make further concessions to the deal they have rejected.
Tuesday's defeat paved the way for two more crucial votes today and Thursday as British lawmakers are set to vote on whether the United Kingdom leaves the European Union without a deal and then to vote on whether to revoke Article 50 - a two-year-long process for any leaving European Union member to complete.
"We must take what now seems to be the more hard route but in the end the one that preserves our self-respect", said former foreign minister Boris Johnson, a favorite to succeed May if she steps down.
This amendment requires the Government to stop Brexit completely, by revoking Article 50, the UK's notice of intention to leave.
The EU said there would be no more negotiations with London on the Withdrawal Agreement, struck with Mrs May after Two-and-a-half years of negotiations.
Opposition Labour leader Jeremy Corbyn also urged parliament to vote down May's plan.
Former minister Edward Leigh said: "You may not like the deal, it's not flawless, but it delivers Brexit and let's go for it".