DUP leader Arlene Foster said yesterday that the EU must face up to reality if a "sensible" Brexit deal is to be agreed.
The Fermanagh MLA said she didn't expect the EU to "roll over" to UK demands, but insisted that it must recognise the strength of feeling in the House of Commons and ditch the "toxic backstop".
She made the comments in a speech to party members in Kesh, just a few miles from the border.
Mrs Foster described the week's events at Parliament, where MPs voted for an "alternative arrangement" to replace the backstop as "good progress".
"It was a massive step forward for the party to see a majority in Parliament also calling for such changes," she said.
"A clear message was sent to Brussels that the backstop is the problem."
It remains unclear whether the EU will reopen negotiations on the withdrawal deal, with the Irish Government's Europe Minister Helen McEntee earlier saying that Dublin would "absolutely not" accept that. Mrs Foster conceded that the EU are "tough negotiators".
"I don't expect them to roll over within hours," she said.
"But they must face up to reality.
"The blockage to getting a deal is the backstop, therefore there must be sensible engagement and a pragmatic approach.
"Here in Kesh we are within walking distance of the border.
"Local people travel to and fro across the border multiple times every day.
"It is quite disgraceful for some in Brussels to exploit genuine fears by spinning tales of border posts, troops and queues.
"No one is building border checkpoints. No one is sending troops to the border either.
"Such talk is foolish and careless.
"Let's focus on getting a sensible deal which works for Brussels, Dublin and London."
Speaking from Brussels yesterday, Ulster Unionist MEP Jim Nicholson also called for a different approach from the EU in order to reach a workable deal.
The MEP, who was first elected to the European Parliament in 1989, said: "There are real dangers of a no-deal situation, so with less than 60 days before the UK's departure from the EU I would urge a more constructive and positive approach from the EU leaders in the coming days and weeks.
"I have been clear, there is a problem with the backstop, not least that it is in direct contradiction to the principle of consent as enshrined within the Belfast Agreement. That needs to be fixed.
"But I am firmly of the view that no problem is insurmountable, and I believe that the EU wants to agree a workable deal."
Mr Nicholson said he had detected a change in tone from European Commission president Jean-Claude Juncker.
"Although time is running out, nothing is insurmountable and common sense must prevail," the veteran politician said.
Meanwhile, a Cabinet minister warned MPs that they may not be re-elected to Parliament if they block Theresa May's Brexit agreement and force the UK to crash out of the EU without a deal.
Liam Fox said politicians would have "little cover when they next face the voters" if their actions led to a no-deal exit.
Mr Fox became the latest frontbencher to suggest Britain's withdrawal may have to be delayed.
The International Trade Secretary said Downing Street's insistence that the UK will leave the EU on March 29, and suggestions by Foreign Secretary Jeremy Hunt and Commons Leader Andrea Leadsom that the exit date could be pushed back, were not "incompatible" stances.
"There would be a huge difference between an extension to Article 50 because we hadn't reached an agreement, or a short delay because we had reached an agreement and needed the legislation to implement it," he said after a speech in London.