"What is necessary is for the House to reflect on what members want in terms of their responsibility to come to a decision on this matter".
With just over 100 days until Britain is due to leave the EU, May faced accusations from some lawmakers that she was trying to force a deeply divided parliament into backing her deal by running the clock down to exit day. It will be Ms Sturgeon's third visit for Brexit talks in a month.
The Labour leader criticised Mrs May for not offering MPs a chance to have their say before Christmas, amid expectations the vote will take place in the week beginning January 14. At the end of her statement, however, Mr Corbyn changed his mind, catching his own deputy leader off guard.
"Avoiding "no deal" is only possible if we can reach an agreement or if we abandon Brexit entirely", she said.
"We will vote against Labour in any confidence motion". "When there are only three months left to avert disaster, that's really not excellent tactics", she added.
Some in Labour argue that May would have to resign as prime minister if she lost.
"A new public vote would be different from the referendum in 2016 because we now know more about what Brexit means", said Margaret Beckett, an MP from the main opposition Labour Party and "People's Vote" supporter.
To a look of bewilderment from Theresa May, Greening said that the prime minister was "not allowing debate".
Image Brexit Secretary Stephen Barclay is among those at cabinet
Updating the Commons on a turbulent summit in Brussels last week, Mrs May told MPs that "some of the resulting exchanges at this Council were robust".
Mrs May spent the end of last week in Brussels, saying she was focused on getting the additional assurances from European Union leaders demanded by MPs to address concerns over the Northern Irish "backstop".
"We're certainly not intending to have a no deal Brexit, but parliament does need to vote for a deal, otherwise the legal default position is we will head for no deal", she said.
May's spokesman said: "In relation to an indicative vote, there are no plans to hold one".
Other cabinet ministers are also reported to favour a scenario of asking MPs to vote on options, which could include a no-deal Brexit, a second referendum, and a "Norway option" to keep closer economic ties with the EU.
The SNP's Westminster leader Ian Blackford said it was "time to call time on this government" and taunted Mrs May: "Where is the leadership?" She accused the premier of trying to halt debate.
Some members of the Cabinet are urging the Government to ramp up planning for a "no-deal" Brexit - a chaotic outcome that could see gridlock at United Kingdom ports, planes grounded and shortages of essential goods.
Ministers will be presented with three options at a meeting on Tuesday morning, to wind down preparations, keep them at a similar level or step up preparations, one cabinet source said, with the latter nearly certain to be chosen.