MPs across Parliament have angrily accused ministers of ignoring the will of the House after they said they would only release a "full reasoned political statement" on the legal position.
If the motion is approved, a cross-party committee of parliamentarians would be tasked with investigating the alleged contempt and considering whether to recommend a punishment.
"This is, after all, not a general election and the Government or the opposition can not be allowed to play fast and loose with representative democracy", they said.
The latest row erupted as it was reported the Attorney General Geoffrey Cox - who is due to make a statement to the Commons today - had warned the United Kingdom could be tied to the EU customs union "indefinitely" through the Northern Ireland "backstop". I fully accept that.
The Government is to publish a command paper on the legal advice on the Brexit deal, the Prime Minister's official spokesman said.
We have been left with no option but to press ahead with contempt.
The Devon MP went on: "I ask the House to understand that it is only that consideration that is motivating me and this Government in declining at this stage to break the convention that applies to both sides of the House when they are in government".
May's government is also facing a battle in Parliament over confidential advice from the country's top law officer about the Brexit deal.
She emphasized that her job was making sure that the government takes the measures that the people demanded.
A video grab from footage broadcast by the U.K. Parliament's Parliamentary Recording Unit (PRU) shows Britain's opposition Labour party Brexit secretary Keir Starmer speaking during the Legal advice on the European Union withdrawal agreement debate in the House of Commons in central London on November 13, 2018.
Solicitor General Robert Buckland told BBC's Newsnight it was a "complete diversion" and a "concocted parliamentary parlour game that should be stopped".
"I wouldn't say it's a probability, but it's a likelihood that's growing fast".
The Conservative prime minister has consistently refused to say what she plans to do if - as widely predicted - the British Parliament rejects the deal her government reached with the EU.
Over the coming days she will deploy senior Cabinet ministers to make the case, with Chancellor Philip Hammond, Foreign Secretary Jeremy Hunt and Home Secretary Sajid Javid expected to appear at the despatch box.
Labour's official policy is to call for a General Election if Mrs May fails to get her Brexit plan through Parliament.
Adding to pressure on Mrs May, it was reported that the PM's chief Brexit adviser secretly warned her that the Northern Ireland "backstop" agreed in her deal with Brussels was a "bad outcome" for Britain. On Monday they delivered petitions to Downing Street signed by one million people.
Under the PM's current deal, the backstop would see Northern Ireland remaining aligned to some rules of the European Union single market, if an alternative solution can not be found by the end of the transition period in December 2020.
The paper reported on a letter sent by Cox, in which the top law officer said: "The [backstop] protocol would endure indefinitely" - and claimed Britain would only be able to lose the backstop through a trade deal, which could take years to reach and on which the European Union would hold a veto. "I'm prepared to lend my support to this agreement because I do not believe that we're likely to be entrapped in it permanently".