A cross-party Brexit deal will need to include a second referendum in order to receive the backing of Labour MPs, Sir Keir Starmer has said.
The shadow Brexit secretary warned it was "impossible" to see how an agreement between the Conservatives and Labour could clear the Commons unless it guaranteed the deal would be put back to the public for a "confirmatory vote".
Sir Keir made the comments ahead of crunch talks between Cabinet ministers and senior Labour figures on Monday, although speculation was growing over whether the negotiations will succeed.
Speaking to The Guardian, the leading Labour negotiator said his colleagues and the party leadership would have to decide "in the coming days" if it was worth continuing with the talks.
Meanwhile, The Times reported that the Prime Minister has been urged by Cabinet ministers to pull out of the talks and move to indicative votes by MPs.
Chancellor Philip Hammond is said to be among those who have lost faith with the plan to strike a cross-party deal, while on Sunday Education Secretary Damian Hinds expressed support for finding a "stable majority" by allowing MPs to vote on different options.
On Monday, foreign secretary Jeremy Hunt seemed to rule out including a second referendum in any cross-party deal.
"From a Conservative point of view, we've always said that we think that would be a betrayal of what people voted for, and we want to implement the first referendum,” he said.
"But let's see where these talks go to. We are talking to the Labour leadership, and we have had very, very detailed discussions.
"People have been pessimistic right from the outset that these discussions weren't going to go anywhere, but they have actually continued.
"So we have to see what happens this week. This is a crunch week."
DUP leader Arlene Foster warned a confirmatory Brexit referendum would place democracy at risk.
She also criticised Mrs May for lacking the vision of a strong United Kingdom post-Brexit.
"What people want to see is democracy being respected,” said Mrs Foster.
“Unfortunately it hasn't been respected and we have a Remain parliament, therefore parliament has not been able to deliver on Brexit in the way it should have been delivered upon.
"We have a prime minister frankly who doesn't have the vision for the United Kingdom post Brexit that we all want to see. We want to see a United Kingdom that is strong post-Brexit and has a close relationship with Europe."
"We have to deliver on the wishes of the people - democracy is at risk here if we do not respect the wishes of the people in the referendum," she said.
Labour MP Stephen Kinnock told BBC Radio 4's World At One programme: "What would be a real shame is if the talks are failing because they are being torpedoed by an additional red line that Labour is bringing in around a second referendum.
"If you try to insert a second referendum into these talks they won't get through because the Conservatives will not whip their MPs to support it."
In the wake of dire local election results for the Tories and Labour and looming European elections - which could see Nigel Farage's newcomer Brexit Party make unprecedented gains - both parties are under pressure to make progress on Britain's EU departure.
"I've made it clear that at this stage, at this 11th hour, any deal that comes through from this government ought to be subject to the lock of a confirmatory vote," Sir Keir said.
The shadow minister said that "probably 120 if not 150" of the party's 229 MPs could vote against the deal unless it was linked to a second referendum.
"If the point of the exercise is to get a sustainable majority, over several weeks or months of delivering on the implementation, you can't leave a confirmatory vote out of the package," he said.
Sir Keir signalled that Labour expects movement from the Government this week in order to keep the talks on track, telling the paper it "would be wrong in principle to use up much more time simply exploring each other's positions".
"I do think we do probably in the coming days need to make that assessment."
The issue of a confirmatory referendum has been an internal battleground within Labour ranks, with Sir Keir pushing for one but shadow business secretary Rebecca Long-Bailey, also part of the negotiating team, less keen.
Sir Keir highlighted how the party lost 200 lost seats in this month's council elections, which he said were a sign Labour was losing the trust of Remain as well as Leave voters.
The party's deputy leader, Tom Watson, is expected to call for a second vote in a speech on Monday.
Mr Watson will reportedly invoke the late Labour leader John Smith, saying the heavyweight would have backed a "people's vote as a way out of this destructive mess".
The Sun says Mr Watson will tell the Fabian Society that Mr Smith, who was tipped to become prime minister before his death 25 years ago, saw "anti-EU sentiment" as "wrong-headed".
The BBC reported that Mr Watson will "plead" with voters to back Labour in next week's European Parliament elections, despite the party's Brexit stance.
"There are only two forces that can win this election - that nasty nationalism of the Farage Brexit Party, or the tolerant, compassionate outward-looking patriotism of the Labour Party," he will say.
A ComRes general election poll published on the weekend found Mr Farage's Brexit Party had overtaken the Tories for the first time, taking a one-point lead.
That level of support would see the Brexit Party win 49 seats, becoming the UK's second biggest party after Labour, with 137.
Speaking to the BBC Radio 4 Westminster Hour on Sunday night, the Chancellor's parliamentary aide, Huw Merriman, said the Tories will suffer "an absolute mauling" in next week's European Parliament elections.
"The public will blame the Conservative government because we were the party that brought forward the referendum," said Mr Merriman, who backs a second referendum.
"And so for those that didn't want it and wanted Remain, they'll blame us for having tried to take us out. And for those that voted to leave, they'll blame us for having not got the country out of the EU.
"We're at the perfect storm, so yes, I think we'll get an absolute mauling."