The brinkmanship comes with Britain three weeks away from crashing out of the EU after 46 years with very few arrangements in place
Britain and the EU were at loggerheads on Friday as Prime Minister Theresa May's call for "one more push" to secure a Brexit deal was answered with an offer that London immediately spurned.
With time running out, May pleaded for movement from Brussels to help get a Brexit deal over the line in time for Britain's looming exit from the European Union - scheduled for March 29.
British MPs overwhelmingly rejected the deal when it was first put to them in January - with many citing the controversial Irish "backstop" clause. A second parliamentary vote will take place on Tuesday.
The backstop would keep the whole UK in a customs union with the EU in order to keep the land border between the UK's Northern Ireland and the Republic of Ireland free-flowing.
In an offer aimed at changing the dynamic, the EU's chief Brexit negotiator Michel Barnier proposed that the British mainland could leave the bloc's customs union after the divorce, though Northern Ireland would stay in.
However, fearing for the integrity of the United Kingdom, May has previously ruled out arrangements that would mean different rules applying in Northern Ireland than in the rest of the UK.
Barnier's new gambit was swifty rejected by Britain's Brexit Secretary Steve Barclay.
"With a very real deadline looming, now is not the time to rerun old arguments," he tweeted.
"The UK has put forward clear new proposals. We now need to agree a balanced solution that can work for both sides."
The brinkmanship comes with Britain three weeks away from crashing out of the EU after 46 years with very few arrangements in place.
Fresh negotiations between British and EU envoys ended in acrimony on Wednesday and May still lacks the assurances she has been seeking to get her deal approved by MPs on Tuesday.
'Moment of crisis'
May told an audience of factory workers in the Leave-backing North Sea fishing port of Grimsby that Britain may never split off from the other 27 nations if Brussels fails to help her now.
The deal "needs just one more push to address the final, specific concerns of our parliament," May said.
"Because if MPs reject the deal, nothing is certain. It would be at a moment of crisis."
As it has no unilateral exit clause, some lawmakers in May's Conservative Party fear that the backstop plan would keep Britain trapped long-term in a customs union with the EU.
May wants a written guarantee from Brussels that this will not be the case. EU officials say the backstop must stay in place until a new trade deal is signed between London and the bloc - no matter how long that takes.
EU ambassadors met in Brussels on Friday to discuss how they might proceed ahead of next week's crucial events in London.
Following the meeting, Barnier said on Twitter that the EU would give the British mainland "the option to exit the single customs territory unilaterally."
However, "the other elements of the backstop must be maintained to avoid a hard border," said Barnier, in reference to alignment between Northern Ireland and the EU-member Irish Republic.
"The EU will continue working intensively over the coming days to ensure that the UK leaves the EU with an agreement."
Demands 'impossible': Dutch PM
Meanwhile Dutch Prime Minister Mark Rutte said May was seeking "impossible" concessions from the EU.
May has scheduled a potential series of parliamentary votes next week that could include one on Thursday asking the EU to grant London an exit day delay.
But May said such a deferral would create "continuing uncertainty", ruin the business climate and potentially mean that Brexit never happens.
"If we go down that road, we might never leave the EU at all," she said.
"It would let down the more than 17 million people who voted to leave the EU and do profound damage to their faith in our democracy."
A top member of the Conservative Party's pro-Brexit hardcore also warned that there would be no deal done by the deadline without a substantive backstop change.
"If it is some very minor, meaningless tweak then of course we will vote against it," MP Mark Francois said.