MPs are voting on a motion that could oust Theresa May's government from power and start moves towards a general election.
Labour leader Jeremy Corbyn, who tabled the no confidence motion, said the PM's "zombie" administration had lost the right to govern, and they "should do the right thing and resign".
But Mrs May said a general election was simply not "in the national interest".
It comes 24 hours after MPs voted down the PM's Brexit plans by a huge margin.
Closing the debate, Labour's deputy leader Tom Watson said: "She is a prime minister without a majority for her flagship policy, with no authority and no plan B."
But Environment Secretary, Michael Gove, said Mrs May had provided "inspirational leadership".
He launched a scathing attack on Mr Corbyn over a number of his positions on national security issues, saying to loud cheers from Conservative MPs that the country could not have confidence in him as a leader.
Mr Corbyn's motion is backed by MPs from the SNP, Lib Dems, Plaid Cymru and Green Party.
But senior Labour figures accept it is not likely to succeed, as she has the backing of Tory rebels and the DUP's 10 MPs, who less than 24 hours ago helped inflict a humiliating defeat on her.
Labour says further no-confidence votes could follow if this one fails.
Mr Corbyn told MPs: "The prime minister has consistently claimed that her deal, which has been decisively rejected, was good for Britain workers and business… she should have nothing to fear by going to the people."
He added that 2011's Fixed-term Parliaments Act "was never intended to prop up a zombie government", saying that the prime minister had "lost control" and suffered an "historic and humiliating defeat".
Mr Watson added: "I don't doubt that [Mrs May] has sincerely attempted to fulfil the task given to us buy the voters in the referendum. I have no doubt too that she has tried her best and given it her all.
"But she has failed and I am afraid the failure is hers and hers alone.
"We know she has worked hard, but the truth is she is too set in her ways, too aloof to lead.
"She lacks the imagination and agility to bring people with her, she lacks the authority on the world stage to negotiate this deal. Ultimately she has failed."
How did Theresa May respond?
Mrs May told MPs it was Parliament that decided to put the question of European Union membership to the people, "and now Parliament must finish the job".
She said extending Article 50, the legal mechanism taking the UK out of the EU on 29 March, to allow time for an election would mean "delaying Brexit for who knows how long".
She repeated her offer of cross-party talks to find a way forward on Brexit, but has not so far invited the Labour leader to take part in them.
A general election would "deepen divisions when we need unity, it would bring chaos when we need certainty," Mrs May said.
What do other MPs think?
Tory MP for Croydon South, Chris Philip, accused Mr Corbyn of "shameless political opportunism", which put "party interests ahead of national interests".
James Morris, Tory MP for Halesowen and Rowley Regis, said the motion was "merely a tactical device by the opposition to cause chaos".
And Conservative ex-minister Anna Soubry, who wants Mr Corbyn to back another EU referendum, questioned why her party were six points ahead of Labour in a weekend opinion poll, adding: "Could it be because he's the most hopeless Leader of the Opposition that we've ever had?"
But other MPs backed Mr Corbyn, with Labour's Stephen Doughty saying his leader was "absolutely right" to call for a general election "because it is not just the government's record on Brexit which is at stake tonight".
Labour frontbencher Liam Byrne, MP for Birmingham, Hodge Hill, accused Mrs May of building "a cage of red lines" over Brexit.
SNP Westminster leader Ian Blackford accused the government of "seeking to run down the clock" over Brexit and warned that the UK could "crash out" of the EU with no deal.
"The risk of a no deal is something that is unthinkable," he said. "If the government and the prime minister want to drive the bus over the cliff, we will not be in the passenger seat."
Lib Dem leader Sir Vince Cable said 48% of the population who voted to remain in the EU had been "totally disregarded" by the government and Mrs May had an "unwillingness to listen".
He said a general election provided "another route and a welcome one" that could resolve the issue, and he also called for a "People's Vote".
The leader of Plaid Cymru in Westminster, Liz Saville Roberts, who will vote against the government later, added her support for a "People's Vote", and called for the House to come together to make progress, condemning the "pantomime point scoring" taking place.
The DUP's leader Arlene Foster and its Westminster leader Nigel Dodds have both said they will support the government in the confidence vote.
But, speaking after what she described as a "useful discussion" with the prime minister, Ms Foster said "lessons will need to be learned" from the defeat on the Brexit deal.
"The issue of the backstop needs to be dealt and we will continue to work to that end," she added.
When will May budge?
A shift to promising some kind of closer relationship with the EU, whether an actual customs union or something by a similar name, seems to be becoming more likely.
That's not because everyone in the government, let alone in No 10 or in the Cabinet, thinks it's the right thing to do - Liam Fox, whose job it is to pursue an independent trade policy, is not the only one with significant doubts.
But you can see a realistic route of getting that kind of arrangement through the House of Commons.
One former minister involved in trying to persuade the PM to soften up said: "We have three days to push and push her to move, or there won't be anything that can get through."
Former prime minister gives backing
David Cameron, who resigned the day after the UK voted in 2016 to leave the EU, said he hoped, and thought, Mrs May would win Wednesday's vote.
Speaking to the BBC he also insisted he did not regret calling the referendum.
What happens next?
BBC political correspondent Iain Watson says that if the prime minister sees off the challenge, she will begin a series of meetings with "senior Parliamentarians" on Thursday.
He said Mrs May intended to retain her "red lines" - ruling out Labour's demand for a customs union with the EU - with sources suggesting compromising on this would risk cabinet resignations.
However, speaking to BBC Radio 5 Live, Justice Minister David Gauke suggested that the customs union option could not be ruled out, saying: "We have got to engage and we have got to be constructive."
Could the UK now stay in the Customs Union?— BBC Radio 5 Live (@bbc5live) January 16, 2019
Justice Secretary David Gauke refuses six times to say whether Theresa May could now change her #Brexit policy, in an interview with @Emmabarnett.#EmmaBarnettShow pic.twitter.com/SF7z0P9bsm
Earlier Leader of the Commons Andrea Leadsom told the BBC the government was clear that it will not delay or revoke Article 50, although Chancellor Philip Hammond reportedly suggested delaying Brexit in a conference call on Tuesday evening.
How does a no confidence motion work?
By the BBC's head of political research Peter Barnes
Under the Fixed Term Parliaments Act 2011, UK general elections are only supposed to happen every five years. The next one is due in 2022.
But a vote of no confidence lets MPs decide on whether they want the government to continue. The motion must be worded: "That this House has no confidence in Her Majesty's Government."
If a majority of MPs vote for the motion then it starts a 14-day countdown.
If during that time the current government, or any other alternative government cannot win a new vote of confidence, then an early general election would be called.
That election cannot happen for at least 25 working days.
How has the EU reacted?
European leaders reacted to Tuesday's vote with dismay but gave no indication they were willing to make concessions.
Several have warned of increased chances of a no-deal Brexit, which many MPs fear will cause chaos at ports and damage industry.
Michel Barnier, the EU's chief Brexit negotiator, said Brussels "profoundly regrets" how the UK's MPs voted and said it was "up to the British authorities" to indicate how it would move forward.
European Commission President Jean-Claude Juncker urged the UK to clarify its intentions, saying: "Time is almost up."
And European Council President Donald Tusk has appeared to suggest that the UK should stay in the EU.
"If a deal is impossible, and no one wants no deal, then who will finally have the courage to say what the only positive solution is?", he tweeted.
Why did MPs reject Theresa May's deal?
The Commons defeat - the largest in history, by 432 votes to 202 - came as a huge blow for Mrs May.
She had spent two years negotiating the plan aimed at bringing about an orderly Brexit on 29 March, 2019, and setting up a 21-month transition period to negotiate a free-trade deal with Brussels.
But it faced opposition across Parliament, which has never had a majority in favour of Brexit. The UK public voted by 52% to 48% to leave the EU in the 2016 referendum.
Some Remain MPs oppose the deal because they want a further referendum with the option to scrap Brexit, while others accept Brexit will happen but want the UK to have a closer relationship with the EU than currently proposed.
On the other side are MPs who think Mrs May's deal leaves the UK tied too closely to EU rules, while some want to see a no-deal Brexit, which is where the UK leaves the EU without any special arrangements in place.
A key sticking point on the plan remains the Northern Irish backstop - the fallback plan to avoid any return to physical border checks between the country and Ireland. Many MPs argue it could keep the UK tied to EU customs rules indefinitely.
Click here if you cannot see the look-up. Data from Commons Votes Services.
In the run up to the vote, the prime minister tried to reassure MPs from all sides of the House over the controversial backstop - having received new written assurances from the EU that it would be temporary and, if triggered, would last for "the shortest possible period".
But some 118 Conservative MPs - from both the Leave and Remain wings of Mrs May's party - voted with the opposition parties against her deal, while three Labour MPs supported the deal.