The Sunday Times reported that some lawmakers are planning to seize control of the legislative agenda from the government in an act that would allow Parliament to extend the Brexit deadline or even overturn the decision to leave the EU.
MPs are due to return to Westminster on Monday - a day before they will vote on whether to pass or reject the prime minister's divorce deal with Brussels.
May, in a Sunday Express op-ed, said opponents of her deal risk letting down the majority that voted to leave the European Union in 2016.
Mr Corbyn was pressed repeatedly on the BBC's Andrew Marr Show to name a date for when he would table a no confidence vote but refused to.
Jeremy Corbyn has set his sights on taking over Brexit negotiations, confirming he will call a no confidence vote to trigger a general election "soon" if Theresa May's current deal is rejected in parliament.
"I don't like the prospect of a no deal".
If a confidence vote failed, he'd be under pressure to back a second Brexit referendum, risking a backlash from the many Labour supporters who voted to leave the EU. And then, in the 2017 General Election, 80% of you voted for MPs who stood on manifestos to respect that referendum result.
"So those on the Brexiteer side seeking ideological purity with a deal are risking Brexit, because there is a growing risk that events could unfold in ways that (mean) they are leaving the door ajar to ways that increase the risk to Brexit". You have delivered your instructions.
She continued: "When you turned out to vote in the referendum, you did so because you wanted your voice to be heard".
Liberal Democrat Brexit spokesman Tom Brake said: "Chris Grayling has lost the plot".
'Some of you put your trust in the political process for the first time in decades. We can not - and must not - let you down.
"The country does have a right to know what members of parliament are for, not just what they are against, and it's important that the house comes to a view as to what it can back", Barclay said.
One of her predecessors, Sir John Major, called for Article 50 to be revoked as he warned it would be "morally reprehensible" to crash out without a deal.
But he has insisted the United Kingdom should not afraid of a no-deal Brexit, despite forecasts from the Treasury and Bank of England warning that it could trigger an economic crisis worse than the 2008 financial crash.
Mr Blackford said a so-called People's Vote on the terms of Brexit, with an option to stay in the European Union, was another "sensible" option to break the deadlock.
Mrs May faced further opposition to her deal from her former Brexit secretary Dominic Raab.
But officials said Brussels would be in listening mode, and take guidance from the prime minister as to the next steps should she suffer a heavy defeat as is widely expected.