Prime Minister Boris Johnson and the European Union have given themselves a week to agree on a Brexit plan. Otherwise, the U.K. will be heading for either a no-deal exit or another humiliating postponement of its departure from the EU.

While support is building for Johnson’s proposals at home, the EU’s chief negotiator, Michel Barnier, told a private meeting of European senior diplomats that the latest British blueprint for post-Brexit arrangements along the border with Ireland falls far short of his conditions for a deal, three EU officials said.

After more than three years of brinkmanship and bickering, Johnson finds himself in the opposite position to his predecessor -- but one no less risky to his leadership. Theresa May lost her job because she struck an agreement with the EU and couldn’t get it through Parliament.

Johnson’s challenge is to reach a compromise with Brussels without losing his new converts at home.

The EU will make a decision in a week about whether the two sides are closing in on a deal, having demanded the British government come up with a better offer. In a sign of the determination to thrash out an agreement, David Frost, Johnson’s envoy to the EU, immediately resumed talks in Brussels and will continue on Friday. Johnson himself may hold meetings in several European capitals over the weekend, officials said.

The pound is headed for the first weekly gain since mid-September as traders position for a possible breakthrough. Options contracts that deliver gains if the pound rises over the next two weeks are headed for their strongest close since May.

Still, after politely welcoming the proposals on Wednesday, the main European institutions broke cover to criticize the plans.

European Council President Donald Tusk, who spoke by phone to Johnson and Irish Prime Minister Leo Varadkar, said he was “unconvinced” by the proposals. European Commission President Jean-Claude Juncker described them as “problematic,” while the European Parliament, which has a veto over the final deal, said it had “grave concerns.”

A spokeswoman for the British government said it doesn’t accept the downbeat assessment from European leaders and that progress has been made.

Failure to reach a deal would set the U.K. on course for a constitutional showdown with few precedents: Johnson has promised to pull the U.K. out of the EU on Oct. 31 whether the talks succeed or not, while Parliament has already legislated to prevent him pulling the U.K. out of the EU without a withdrawal agreement. A Scottish court will start hearing a case on Friday designed to ensure he complies.

After two missed Brexit deadlines already this year, the clock is ticking louder than ever. It’s now impossible to see a deal being done in time unless Johnson makes fresh proposals, two EU officials said. Barnier told diplomats Johnson’s response needed to be urgent and sustainable.

Johnson’s Brexit plan can’t be negotiated by Oct. 31, Norbert Roettgen, the chairman of the foreign affairs committee in the German parliament said in a tweet. “If U.K. is serious about this, it must seek extension,” he said.

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But in London, as the British parliament debated Johnson’s plan, it became clear that the new deal would receive the backing of Brexit hardliners and those on the pro-EU side of the governing Conservative Party as well as some opposition Labour parliamentarians and the Northern Ireland’s Democratic Unionist Party. The agreement May reached with the EU a year ago was rejected three times.

Indeed, the lukewarm response from the EU caused friction between Belfast and Dublin as politicians traded blows over the plan. Irish Foreign Minister Simon Coveney said his government would never accept any proposal that gives Northern Ireland an effective veto over the measures. DUP leader Arlene Foster accused him of rejecting a “reasonable offer” and “paving the way for a no-deal Brexit.”

The EU believes Johnson’s plan doesn’t work because it leaves Northern Ireland subject to different customs rules from the Irish Republic, and leaves it till after Brexit to work out how to do customs checks on goods traveling between the two countries.

Brussels also doesn’t accept giving Northern Ireland’s assembly a veto over the plan every four years, fearing it could be left with no control over the EU frontier at all. The assembly in Belfast, meanwhile, has been suspended since January 2017 after a dispute between the two main parties, the DUP and Irish nationalists Sinn Fein.

In a sign that all is not lost, it emerged that Johnson may be prepared to consider an alternative plan and keep Northern Ireland in the customs union as long as the EU puts a time limit on it, two people familiar with the matter said.

That idea is not something the EU is formally considering, but officials haven’t ruled out that it could be an element of an eventual compromise.

--With assistance from Dara Doyle, Tim Ross, Jessica Shankleman and Nikos Chrysoloras.