May's office had earlier played down the technical impact of defeat.
A group of 17 Tory rebels inflicted yet another Brexit loss for Mrs May as they joined a majority in the Commons in demanding she set out an alternative strategy within three days of any defeat on her agreement.
MPs have just begun five days of debate on the Brexit agreement ahead of the crunch vote on January 15.
A series of MPs rose to complain that the Government motion should not have been amendable.
British legislators have slashed the time Prime Minister Theresa May's government will have to formulate a plan B if her widely criticised Brexit deal is rejected in a crucial parliamentary vote next week. But there is little indication that many MPs have been swayed and the deal is nearly certain to be defeated on Tuesday. Ms.
The government had been expecting to have 21 days to come up with fresh proposals under those circumstances.
The main source of contention is the plan's safety net "backstop" measure - which would guarantee no hard border is reintroduced on the island of Ireland in the event that post-Brexit trade negotiations between the United Kingdom and the bloc prove unsuccessful.
Tory MPs to speak in favour of the motion included ex-ministers Nick Boles and Sir Oliver Letwin.
Mr Grieve said his amendment was an attempt to "accelerate the process" if the vote was lost so as to avoid the prospects of a no-deal Brexit.
The Commons Speaker faced a backlash from Conservative MPs after selecting an amendment that forces Theresa May to return with a revised European Union exit plan within three sitting days if her original Brexit deal is defeated.
Late on Tuesday, 303 MPs - including more than a dozen former Conservative ministers - voted to restrict the government´s taxation powers in a "no deal" scenario, against 296 who backed May. With less than three months before Britain leaves the European Union, there is no indication the country will have any arrangements in place, with the European Union governing issues such as border controls, banking relations and even whether Britons will be able to use their cellphones in Europe. "She pledged to get these changes over the recess", Jeremy Corbyn pointed out at PMQs today. May's deal or remaining in the EU.
But there is no clear majority for any single alternate course.
May's de-facto deputy said it was a delusion to think the government would be able to negotiate a new divorce deal if Parliament voted down hers.
But she has little room to manoeuvre.
He said: "You said you would serve nine years, there has been the controversy of the recommendations of the Dame Laura Cox inquiry into the House of Commons, you have been defended particularly by two members on the other side about the importance of you being sustained in this position beyond nine years in order to oversee the discussions of the Brexit issue".
May's deal sets out plans for a post-Brexit transition period in which Britain would keep making financial contributions until December 2020. The Tories are also deeply divided.
Numerous Labour MPs also came to his defence, with Labour MP Chuka Umunna tweeting: "In the Commons chamber now watching the spectacle of a bunch of Tory MPs, who argued for Brexit to reassert Parliamentary sovereignty, now objecting to the Speaker selecting a motion to be voted on that would empower the House of Commons".