However, Mrs May did receive some support on Wednesday when Japanese prime minister Shinzo Abe and his Dutch counterpart Mark Rutte both pledged to try and help her win approval for her Brexit deal next week.
The latest parliamentary fireworks come after the anti no-deal MPs defeated the government on Tuesday evening, in a significant show of parliamentary strength against what they feel would be a "cliff-edge" withdrawal from the EU.
A majority of members of Parliament oppose a no-deal Brexit, but it remains the default option if May's deal is rejected.
Opposition to May's deal is spread across the political spectrum, including sections of her own ruling Conservative Party and the 10 Northern Irish Democratic Unionist Party (DUP) MPs her government relies on to command a majority in parliament.
Barry Gardiner, the opposition Labour Party's shadow global trade secretary, said earlier his party will table a no confidence motion in the government if - as expected - Parliament votes down Prime Minister Theresa May's Brexit deal.
Pro-EU Conservative politician Dominic Grieve, who proposed the measure, said it was meant to speed up decisions, to help avoid a no-deal Brexit and "the calamitous consequences that would follow on from it".
But May's spokesman insisted: "We will not be extending Article 50".
The Times understands that Sir Keir Starmer has told the Labour leader that with less than three months to go before leaving the European Union the party's options are limited and it has an obligation not to allow the government to run down the clock on a no-deal Brexit.
John Bercow seized control of the Brexit process from Theresa May and handed it to MPs as the Prime Minister suffered her second humiliating Commons defeat in as many days.
Meanwhile, Business Secretary Greg Clark told the House of Commons that a no-deal Brexit "should not be contemplated".
He said: "That sticker on the subject of Brexit happens to be affixed to or in the windscreen of my wife's vehicle, and I'm sure he wouldn't suggest for one moment that a wife is somehow the property or chattel of her husband".
Lawmakers voted 308-297 in favour of demanding the government come up with an alternative plan within three working days after Tuesday's vote, rather than a planned 21-day limit, a largely symbolic vote aimed at putting pressure on the government.
Mrs May's attempts to win over MPs were further thwarted on Wednesday after the DUP dismissed new assurances over the controversial backstop element of the withdrawal agreement as "meaningless".
But northern Irish politicians were swift to dismiss her proposals to offer Northern Ireland a "strong voice and role in any decision to bring the backstop into effect".
Britain is due to leave the European Union on March 29. That is why we are taking every opportunity possible in Parliament to prevent no deal.
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". But there is little indication that many MPs have been swayed and the deal is nearly certain to be defeated on Tuesday. Ms.