He warned that up to 150 Labour MPs will not back a deal unless they can put it back to the public - with the option to cancel Brexit.
Labour's Brexit chief today publicly demanded a second referendum from the party's talks with Theresa May.
In a major intervention, Sir Keir Starmer warned it will be "impossible" to get any deal through Parliament without a public vote attached. Labour Party, Theresa May
He warned up to 150 Labour MPs will refuse to back a deal unless they can put it back to the public - with the option to cancel Brexit and remain in the EU.
The Shadow Brexit Secretary's call heaps pressure on Jeremy Corbyn as compromise talks between Labour and the Tories limp into their sixth week.
Sir Keir will join Labour and Tory senior ministers again tonight for further talks on a possible customs union between the UK and the EU.
But those talks have been deadlocked for weeks. And now his focus on a second referendum - rejected by Tories and Theresa May - now risks collapsing them within days. Reports today say Remain-backing May loyalists, including Chancellor Philip Hammond, are now saying the talks must be broken up as they are going nowhere.
And Sir Keir said: "I think 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.”
Sir Keir's call for a public vote was backed by deputy Labour leader Tom Watson. Mr Watson said it would be "difficult" to pass any deal without a "confirmatory" second referendum attached.
He said 150 was "around the sort of type of number of MPs" that could demand a referendum from Labour.
Mr Watson suggested late Labour leader John Smith - who died 25 years ago this week - would have.
"John would look at this as not a left or right issue," he told the BBC. "He knew the difference between nationalism and patriotism."
So far Jeremy Corbyn, Labour's conference and the party's ruling National Executive Committee have backed a second referendum - but not on any Brexit deal.
Currently Labour would only back a second referendum if it was on a bad Tory Brexit, or no deal Brexit, or if talks weren't successful in getting the Brexit Labour wants.
Sir Keir made his intervention in an interview with the Guardian.
He said: “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."
He added: “It has got to be something truly deliverable.
“For many of my colleagues, they have made it clear that they will not vote for a deal without a confirmatory vote attached to it.
"So if you want that stable majority, that has to be taken into account. And without it, it is impossible to see how the numbers would stack up.”
Mrs May will put a brave face on the saga today by resuming talks to find a Brexit compromise with Labour.
Her Chief Whip, deputy, Business Secretary, Environment Secretary and Brexit Secretary will hold the talks on Monday evening.
Labour is expected to send Shadow Chancellor John McDonnell, Brexit chief Keir Starmer, business chief Rebecca Long-Bailey and environment chief Sue Hayman.
But privately sources were not expecting a breakthrough after Mrs May refused to accept Labour's demand of a permanent customs union.
Shadow minister Jon Ashworth told the BBC's Andrew Marr Show: "It's not getting very far, but we are still engaging in those negotiations in good faith."
Housing Secretary James Brokenshire today insisted Brexit talks with Labour are "very serious" and he wants to see a positive conclusion to them.
"I think these talks are very serious - we wouldn't have committed all of the time and effort on all sides in relation to this," he told BBC Radio 4's Today programme.
"They have been constructive, they have been detailed and obviously they will resume later today and I very much want to see them concluding positively because ultimately we need to carry a vote in Parliament to see that we leave."