Health Secretary Matthew Hancock said it would be "extremely difficult" but "still possible to deliver Brexit on 29 March with a deal". However, MPs categorically rejected an amendment that called for a second Brexit referendum.
But Parliament could also express its views on alternative options including another General Election, a vote of no confidence or another referendum.
I certainly have the sense that the DUP would like the United Kingdom to leave the European Union with a deal, that they don't want no deal either so at the moment they're in discussions with the British government about how they might approach the next vote but they're discussions that I'm not party to.
European Union leaders on Friday sought clarity from Britain before they consider any delay to Brexit after a series of chaotic votes by MPs just two weeks before the deeply divided country is due to leave the bloc.
She had been forced to offer MPs a vote on delaying Brexit after they rejected her withdrawal agreement by a large margin, for a second time, and then voted to reject a no-deal Brexit.
Quitting the EU after 46 years on 29 March remains the legal default unless EU leaders unanimously grant Britain an extension, with the issue likely to dominate a 21-22 March EU summit in Brussels. May hopes that this can convince enough MPs to start supporting her deal.
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That loss came after a defeat to Barcelona in the Copa del Rey, which saw them dumped out of cup at the semi-final stage. Real Madrid were dealt with a double knockout blow in the summer of 2018 which they clearly haven't recovered from.
May has essentially handed Brexit supporters an ultimatum - ratify her deal by next Wednesday or face a long delay to Brexit that would open up the possibility that Britain never even leaves.
"What we have said is that obviously the British government will need to decide, if they do want an extension, how long they will want it for, and we will be positive and constructive in relation to that, when they put it forward", he told Bloomberg.
Labor's plan to delay Brexit to allow Parliamentary time for MPs to "find a majority for a different approach" was defeated by 318 to 302 votes.
Success would be a remarkable turnaround for May, whose authority has been shredded by a series of defeats in Parliament.
Any delay will require the agreement of all other 27 European Union members, with talks about possible conditions for an extension to take place before next week's European Union summit, which begins on Thursday.
The vote against a no-deal Brexit was non-binding, but investors believe Britain will now avert a disorderly Brexit that would severely damage its economy. "I have a role in the European Parliament", Farage said.