MPs are voting on whether to find ministers in contempt of Parliament over their decision not to release the full legal advice on the Brexit deal.
Opposition parties say by limiting the information released, ministers ignored a binding Commons vote demanding they provided the full advice.
A government attempt to refer the issue to the Commons Privileges Committee was earlier rejected by 311 to 307 votes.
It comes as Theresa May prepares to sell her Brexit deal to MPs.
MPs will vote whether to accept or reject the terms of the UK's withdrawal from the EU on Tuesday 11 December.
It has to be backed by a majority of MPs if it is to come into force.
Meanwhile, the BBC has said it has not been able to reach agreement with Theresa May and Jeremy Corbyn on the format for a proposed televised debate on Brexit next Sunday.
The broadcaster said it was "disappointed" that its "fair and appropriate" proposals for a head-to-head debate between the two leaders followed by a panel discussion including a range of voices and views on Brexit had not been accepted.
The legal advice row
The government's chief legal adviser, Attorney General Geoffrey Cox, published an overview of his legal advice on Monday.
Senior MPs from Labour, the Liberal Democrats, the SNP, the Democratic Unionist Party, Plaid Cymru and the Green Party all signed a motion demanding immediate publication of the full and final advice.
Putting the motion to Parliament on Tuesday, Labour's shadow Brexit secretary, Sir Keir Starmer, said what Mr Cox had told the Commons was "not legal advice" but "simply described the deal".
He added: "The government is wilfully refusing to comply with a binding order of this House and that is contempt."
Commons Speaker John Bercow said late on Monday there was an "arguable case" that a contempt of Parliament had been committed.
However, the government then tabled an amendment to have the issue referred to MPs on the Privileges Committee to investigate whether its response fulfils all its obligations, taking into account any relevant past cases.
Putting the amendment to the House on Tuesday in response to Sir Keir, the leader of the Commons, Andrea Leadsom warned MPs to "exercise caution in this matter".
"The use of this [contempt] motion has happened very rarely in the history of Parliament," she added.
"No honourable member could say in all honesty that the attorney general has done anything other than treat this House with the greatest of respect, there can be no question that he or the government has acted in a manner which is contemptuous of this House."
BBC political correspondent Iain Watson said any defeat over the legal advice would be likely to come as "an unwelcome distraction rather than a disaster" for the prime minister.
"While ultimately a parliamentary committee could decide to reprimand or suspend ministers, it's highly likely no sanction would be applied before next week's crucial vote on the Brexit deal," he said.
MPs seeking to take control of Brexit
Before the main debate on the Brexit deal gets under way, MPs will talk about the procedures involved.
Most of this will be uncontroversial stuff but ex-attorney general Dominic Grieve has put down a significant amendment that, if passed, could potentially tilt the balance of power between government and Parliament.
The amendment, backed by 16 Tories as well as opposition MPs, would change the rules for what happens should MPs vote down Mrs May's deal next week and there is subsequent gridlock.
Instead of the government having to come back to tell MPs what their next steps are - and MPs voting on a "we have seen what the government has said" - they would theoretically be able to vote on "we have seen the government's plans but we want them to do xxx".
The BBC's political editor Laura Kuenssberg said MPs, many of whom want the possibility of a no-deal exit ruled out completely, were asking for the right to tell ministers what to do if there is a second attempt to get the PM's deal through the Commons.
The crunch debate on Brexit deal
Opening what looks set to be the defining moment for her version of Brexit, Theresa May is expected to say the UK is on course for a "better future outside the EU" and that her deal "takes back control of our borders, laws and money".
However, the prime minister faces opposition from MPs on all sides - including both the Leave and Remain wings of her own party - who argue that better deals could be available or that the public should have the final say in a referendum.
Many believe her deal is flawed because of a "backstop" that could keep the UK tied to EU customs rules in the event no future trade deal can be agreed.
Speaking on Monday, Attorney General Geoffrey Cox said that signing up to it was a "calculated risk" but added: "I do not believe we will be trapped in it permanently."
MPs will debate different aspects of the EU agreement over the next week, with a focus on security on Wednesday, the economy on Thursday and the future of the United Kingdom on Monday.
Further details have still to be announced but Mrs May will kick off proceedings by telling MPs: "The British people want us to get on with a deal that honours the referendum and allows us to come together again as a country, whichever way we voted."
Mrs May will argue her Brexit deal delivers on her commitments to end free movement and the jurisdiction of the European Court of Justice.
It will leave Britain "as a globally trading nation, in charge of our own destiny and seizing the opportunities of trade with some of the fastest-growing and most dynamic economies across the world", she will add.
Mrs May will say future trade talks with Brussels will also ultimately result in "a new free-trade area with no tariffs, fees, quantitative restrictions or rules-of-origin checks - an unprecedented economic relationship that no other major economy has".
Labour is threatening a vote of no confidence in the government as part of a move to trigger a general election, if Mrs May is defeated on 11 December.
The party is in favour of Brexit but against Mrs May's deal, which it argues will harm industry and cost jobs. It wants to delay Brexit to negotiate a better deal with Brussels.
So could Brexit legally be cancelled?
The UK should be able to unilaterally cancel its withdrawal from the EU, according to a top European law officer.
The non-binding opinion was delivered by the European Court of Justice's advocate general.
A group of Scottish politicians has asked the court whether the UK can call off Brexit without the consent of other member states. The Court of Justice will deliver its final ruling at a later date.
While the advocate general's opinions are not binding, the court tends to follow them in the majority of its final rulings.
The advice from advocate general Manuel Campos Sanchez-Bordona was that if a country decided to leave the EU, it should also have the power to change its mind during the two-year exit process specified in Article 50 of the EU treaty.
And it should be able to do so without needing the consent of the other 27 member states. As things stand the two year deadline under the Article 50 process means Brexit will happen on 29 March, 2019.