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Andrea Leadsom, the leader of the House of Commons, said Bercow should publish the advice he received from the Commons clerks.
But EU leaders have refused to budge, insisting that the withdrawal agreement can not be renegotiated.
"The amendment doesn't affect the normal operations of the Treasury. but it does make it harder for the government to drift into no deal without parliament being able to direct it", Yvette Cooper, the MP who introduced the amendment, told the Guardian.
With less than three months before Britain leaves the EU, May has warned lawmakers if they do vote down her deal, they would be opening the way for a disorderly exit or for Brexit not to happen at all.
There were unusual scenes as the speaker, John Bercow, accepted an amendment that forces the May government to come up with a Plan B within three days of the withdrawal agreement being voted down on January 15.
When asked about the business secretary's comments, Downing Street said the prime minister would not use such language to describe a no-deal Brexit.
It is likely to prompt an angry response in Brussels, which has repeatedly rejected efforts to put a time limit on the backstop, meant to avoid a hard border in Ireland if no wider trade deal has been agreed.
There's no guarantee Labour could marshal the majority support in Parliament needed to topple the government - and even if it did, a new election would not automatically stop the Brexit countdown clock.
"But I do not think that no deal will be good for this country and I am committed to making sure that we find an alternative".
But a Conservative MP who had been expected to reject the deal, George Freeman, said during Thursday's debate that he would now back it "with a heavy heart" because, he said, the prospect of leaving without a deal was "unconscionable".
A majority of Prime Minister Theresa May's Conservative Party members oppose her Brexit deal with the European Union saying it does not respect the result of the 2016 Brexit referendum, according to a survey published on Friday (4 January).
The vote significantly increases the possibility of Theresa May calling for either a second referendum of a snap General Election to break the deadlock.
Responding to the vote, Brexit minister Stephen Barclay told parliament it was the government's intention to act quickly if it lost Tuesday's vote.
Prime Minister Theresa May is likely to win over either the Brexiteer or Remain faction in parliament to see her deal pass, this outcome will boost Pound Sterling we are told.
Mr Bercow hit back, saying: "There was nothing arbitrary about the conduct of the chair yesterday".
We can leave the European Union under the terms of some version of the prime minister's bad deal or we can keep all our rights, powers, influence and op-outs in our current deal as full members of the EU.
A former director of legislative affairs at Number 10, Nikki da Costa, said: "More than anything this is not just overturning something the House accepted in a business motion, it is overturning the EU Withdrawal Agreement and procedure voted on and approved in both Houses with much debate and scrutiny, and indeed which Grieve accepted on floor of the House".
Britain's de-facto deputy prime minister, David Lidington, said politicians must abandon "fantasies about magical alternative deals that are somehow going to sort of spring out of a cupboard in Brussels".