The government has offered to publish its most recent internal assessment of the impact on business and trade of a no-deal Brexit, in the face of a possible Commons defeat.
Ministers are said to have seen the documents prepared by the civil service, but they have not been made public.
MPs were set to vote on forcing the government to release the papers on Thursday afternoon.
Pro-EU Tory MP Anna Soubry, who had tabled the amendment, said if the government did not publish the impact assessments as promised she would once again try to force its hand.
Speaking in the Commons, Soubry said MPs who were comfortable with no-deal should want to see the documents in order to be “better informed” about the “dangers”.
“It really would be to the eternal shame of this party if it were to continue to support a no-deal Brexit,” she said.
Several Tory ministers are reported to be considering resigning in order to try and prevent a no-deal exit.
But pro-Brexit Conservatives have demanded Theresa May, at the very least, keep no-deal on the table as a serious option.
With just 43 days to go until exit day, the prime minister has been accused by Labour of “running down the clock”.
The party fears May wants to bounce parliament into backing her deal at the last minute as the only way to avoid crashing out of the EU with no deal.
Ministers have not ruled out holding the crunch meaningful vote on whether to accept or reject a deal as late as the last week of March.
Shadow Brexit secretary Sir Keir Starmer said the threat of a no-deal was a smokescreen designed to force MPs into backing May’s deal.
He said he did not think the prime minister would really take the UK out of the EU without a deal because of her “deep sense of duty”.
But Oliver Letwin, the former Tory cabinet minister, said he had come to the “terrifying” conclusion that May was now ready to “head for the exit door without a deal”.
Earlier today, car giant Ford warned that leaving the EU without a deal next month would be “catastrophic” for the UK’s auto industry.