In Brussels for pre-summit briefings, Ireland's foreign and trade minister Simon Coveney warned a deal must be found by the October summit instead of being allowed to drag into November.
Ahead of this week's Informal Summit in Salzburg, EU officials in Brussels have been running through the agenda as the European heads of state and government gear up for talks ranging from Brexit to the Skripal poisoning in the United Kingdom earlier this year.
Khan said the "sensible thing" would be for the prime minister to call a general election if she did not have support for any Brexit deal.
UK Labour Party leader Jeremy Corbyn leaves the stage after delivering a speech at Queens University in Belfast, Northern Ireland, May 24, 2018.
The EU's involves Northern Ireland following EU law on customs and goods, a plan May has said no British prime minister could ever accept.
He also said Mr Barnier's suggestion that the Irish border issue be "de-dramatised" was about trying to move away from language like creating a border in the Irish Sea.
May says it will not happen because over the next couple of years, Brussels and London will work out a deal to ensure seamless UK-EU trade.
"We are clarifying which goods arriving in Northern Ireland from the rest of the United Kingdom would need to be checked and where, when and by whom these checks could be performed", he said.
"We need to challenge the assumptions of both these Irish backstops, or we are heading full throttle for the ditch with a total write-off of Brexit".
Committee chairman Hilary Benn said that with time running out to secure a withdrawal agreement there were "significant problems yet to be resolved", with the Irish border backstop the main sticking point.
My Brexit plan or crash out of EU, says Theresa May
European Union officials and many British experts are also anxious that a no-deal Brexit would damage economic and financial ties between the world's biggest trading bloc and one of the world's largest economies.
Mr Barnier's comments came after Taoiseach Leo Varadkar had earlier told the Dail in Dublin: "I do not anticipate there will be any change to the EU's position or any change to our negotiating guidelines".
The UK needs to "urgently" find draw up an alternative to Theresa May's Chequers to avoid crashing out of the European Union with a "chaotic and damaging" Brexit, MPs warned in a new report on Tuesday (18 September).
But EU officials are also minded not to paint May into a corner, aware that she faces increasing opposition to her plans in her Conservative Party and needs a victory of sorts to try to persuade a reluctant parliament to back a deal.
DUP Brexit spokesman Sammy Wilson had previously voiced unhappiness with some aspects of the plan.
Christine Lagarde, the IMF's managing director, told a news conference at the Treasury in London: "Those projections assume a timely deal with the European Union on a broad free trade agreement and a relatively orderly Brexit process after that".
Yesterday the DUP, on whose support Mrs May relies for her Parliamentary working majority, called on the European Union to clarify its plans.
He branded people who continually kept pouring cold water on the idea of tech-based fixes "pathetic parrots".
If any spot check revealed discrepancies in the goods being carried, the firm would lose its "trusted trader" status.
Chancellor Sebastian Kurz of Austria - which holds the bloc's six-month rotating presidency - will open the two-day summit on Wednesday evening in Salzburg.