Theresa May has declared it is the EU's turn to compromise, as she sat down for crunch talks with European leaders.
The prime minister said they had to "evolve their position", just as the UK had done.
Arriving at the Salzburg summit, Mrs May backed her Chequers proposal, saying it was the "only credible" option to ensure frictionless trade and no hard Irish border.
Speaking back home, Brexit Secretary Dominic Raab also said that without reciprocal concessions by the EU, there would be a "lose-lose" outcome for both sides.
He admitted the Chequers proposal was "not perfect", but it was the "most credible one".
It came hours after European Council President Donald Tusk announced Britain had to "rework" its suggestions and suggested a mid-November summit to attempt to finalise a deal.
He also announced plans to call a summit of EU leaders in mid-November to attempt to finalise a Brexit deal.
Mr Tusk declared: "The Brexit negotiations are entering their decisive phase.
"Various scenarios are still possible today but I'd like to stress that some of Prime Minister May's proposals from Chequers indicated positive evolution in the UK's approach."
Despite noting that the UK was prepared to work closely with the EU on security and foreign policy post-Brexit, Mr Tusk said there still need to be changes to Britain's approach, particularly on the future of the Irish border and economic co-operation.
Proposals in these two areas "will need to be reworked and further negotiated," Mr Tusk said, noting that while there was "more hope" there was "less and less time" to reach a deal.
Mrs May's trip to Salzburg is the first time EU leaders have met since she published her Chequers proposals in July - the cabinet deal seeking to maintain free-flowing trade in goods by maintaining common rules with the EU.
In talks at Salzburg's Mozarteum University, the PM will this evening try again to persuade EU leaders her much-derided plan is the right way forward.
A senior Downing Street source said the PM would tell EU leaders in Salzburg that Britain was proposing "a fair arrangement that will work for the EU's economy as well as the UK's".
The source told the Reuters news agency: "To come to a successful conclusion, just as the UK has evolved its position, the EU will need to do the same.
The plan envisages Britain retaining common EU rules for goods, but not services.
It sparked the resignations of David Davis and eventually, Boris Johnson - and the PM is coming under increasing pressure from her backbenchers to "chuck Chequers".
Mr Johnson has led calls for Mrs May to change course and Mr Davis will use a speech tomorrow to attack her Chequers proposals.
The former Brexit secretary will describe the plan as a "non-starter" which breaks all of the PM's red lines in the negotiations.
"The EU is often correctly described as having a democratic deficit. But Chequers is devoid of democracy altogether," Mr Davis will say.
"This is why many of us will shortly be presenting an alternative plan which will outline a more ambitious vision."
But Mrs May is, so far, sticking to her guns, warning her party it is a straight choice between her deal or no deal.
And in apparent bid to smooth the road to an agreement, Brussels' chief negotiator Michel Barnier said on Tuesday he was prepared to put forward a new offer on the Irish border.
Mr Barnier said he wanted to "de-dramatise" the issue, suggesting the majority of checks on imports and exports could take place away from the border itself.
But the DUP, which props up the minority Conservative administration at Westminster, dismissed Mr Barnier's proposals.
Deputy leader Nigel Dodds said: "Despite the talk of 'improvements' the backstop being insisted upon by the EU would mean a different regime for Northern Ireland compared to the rest of the UK.
"It still means a border down the Irish Sea, although with different kinds of checks.
"The fact is that both Theresa May and the Labour Party have said no British prime minister could accept such a concept.
"It is not just unionists who object."
Labour's Owen Smith, a former shadow Northern Ireland secretary who is backing the Best for Britain campaign for a second EU referendum, said the DUP's riposte had "sunk Barnier's improved offer on Northern Ireland before he has even floated it".
The PM has also been steadfast in her opposition to a second referendum on the exit deal Britain agrees with the EU.
And in a bid to bring wavering MPs (BSE: MPSLTD.BO - news) into line, Treasury minister Mel Stride suggested opponents of Chequers could end up bringing about a second referendum or a "no-deal" scenario.
He told Sky News' All Out Politics programme: "When we have a firm deal on the table, I suspect that those to the right of the party - the pro-Brexit wing - will be very concerned that if that deal does not prevail, they will end up in the situation where we could have a second referendum or we could end up not leaving the EU altogether, so there is a danger of that happening if Chequers does not prevail.
"I think those on the other end of the spectrum will equally be very concerned that if Chequers does not prevail, we could end up in a no-deal situation."