Mr Barnier had already ambushed the UK by re-tabling old demands for the UK to respect all laws the EU might pass in the future.
The move would effectively bind Britain to EU laws, under the threat of huge tariffs if they were broken.
The two sides are now expected to draw up a list of the remaining differences between them ahead of the PM travelling to Brussels.
Some close to Mr Johnson say a breakthrough could still be a week away given the differences between the two sides and he may not travel to the continent until the weekend.
A Whitehall source said: “There’s no real reason this can’t happen next week.
"The talks need a political injection and we should not be bound by time constraints on when that is. We need it to work so it should come at the right time."
Countless self-imposed deadlines for a deal have now been missed, but both sides must ratify the new trading arrangements before 1 January 2021 or face border chaos and the economic blow of a No Deal.
After a “working dinner” of burgers for the two sides in Brussels on Sunday night, talks went late into the night.
But both sides conceded that Brit chief negotiator David Frost and his Brussels counterpart were “going round in circles” by Monday afternoon.
NO DEAL AHEAD? Hopes of a deal had briefly soared when Downing Street confirmed they were willing to drop contentious plans to break international law by ripping up some parts of last year’s divorce deal with Brussels if talks collapsed.
But the controversial Internal Market Bill that would give ministers the power to override the terms of last year’s “oven ready” Withdrawal Agreement may now be watered down in a move that was seen as a big olive branch to the EU.
Brussels had been infuriated by the threat, but some ministers had privately admitted it was merely a hardball negotiating tactic
Earlier in the day Ms von de Leyen had spoken with Angela Merkel and Emmanual Macron.
There is continued anger on the British side towards the French President who many blame for last minute toughening up of EU demands.
Meanwhile gloomy EU diplomats instead blame an 11th hour demand from the UK on fishing for slowing down progress.
One told The Sun: "These are going to be decisive hours for the future of UK-EU relations and we’re at the make it or break it moment."
EU sources said Mr Barnier had briefed member states on Monday morning that "we are not far from the very endgame, but we cannot go further than Wednesday.
“I can't guarantee we will reach an agreement tonight, we might still have to negotiate tomorrow", he added.
Last night the two leaders said: “As agreed on Saturday, we took stock today of the ongoing negotiations.
We agreed that the conditions for finalising an agreement are not there due to the remaining significant differences on three critical issues: level playing field, governance and fisheries.
What are the sticking points in Brexit talks?
LEVEL PLAYING FIELD: Brussels wants a shared set rules and standards to ensure businesses in the UK do not have an unfair advantage over their competitors. The UK has said it won't lower its standards, but wants to be able to set its own rules.
GOVERNANCE: Who decides what happens if the terms of the deal are breached? The EU wants an European body to decide the terms, but the UK aren't keen on this and want an independent arbitrator to have the final say.
FISHING : The EU wants continued access to Britain's fishing waters after we leave. It's claimed Britain would be happy with a three year deal to phase out access, but the EU are pushing for ten. One of the key referendum claims was that Britain would be able to take back control of our borders - including fish - when we leave the EU.
EU chief Brexit negotiator Michel Barnier pictured in Brussels today Credit: AFP or Licensors Britain's chief negotiator David Frost leaving talks in Brussels earlier Credit: AP:Associated Press
“We asked our Chief Negotiators and their teams to prepare an overview of the remaining differences to be discussed in a physical meeting in Brussels in the coming days.”
"A UK source added: "The Prime Minister still thinks there is a deal to be done but it has to recognise what people voted for twice. One in 2016 and again last year.”
Boris Johnson's negotiating team to go back into crunch talks as 'no breakthrough is made' says EU chief