The European Union and Britain have given themselves a few more weeks to break the deadlock in their Brexit talks but for Brussels the delay seems mainly about Prime Minister Theresa May dealing with critics back in London.

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An accord sketched by officials from both sides last weekend stalled because May's fractious government rejected a "backstop" insurance clause the EU wants in case future talks fail to forge a trade pact that avoids customs posts on the Irish border.

An EU offer to extend a status-quo transition period by a year to end-2021, keeping Britain in a customs union to diminish the chances of the backstop being triggered, was not enough.

EU negotiator Michel Barnier pledged at a summit to keep working "calmly and patiently". But many EU leaders see the main negotiations to be had now as being among May and her allies in London, possibly only after she gets a budget through parliament early next month. They see little scope now for the EU to move.

"We took our steps. We need to know what the other side wants - finally," said Lithuanian President Dalia Grybauskaite.

Britain is due to leave the EU on March 29, 2019, less than three years since Britons voted for an exit in a referendum.

"This is pretty much it," an EU diplomat said of the weekend offer, which included a longer transition to give time for a customs deal. "This is the deal - if ever there's to be one."

French President Emmanuel Macron noted the tricky "political balance" May faces at home -- her vital Northern Irish allies say the EU's backstop, by keeping Northern Ireland alone in the EU customs area, would break up the United Kingdom; and Brexit hardliners insist the UK must leave the EU customs union soon.

Acid Test

All governments insist, though, that they want a deal in the coming weeks that can avoid chaos when Britain leaves in March.

There are limited ways to salvage an agreement.

The EU is firmly behind Ireland. It says any "hard border" infrastructure on its frontier with the British province of the island would revive sectarian conflict. Many small EU states see the willingness of big powers to risk trade with Britain to protect Ireland as an acid test of the value of EU membership.

That limits May's scope for rejecting any backstop at all.

Her solution so far has been to offer to keep the British mainland also inside EU customs rules for a time. But the EU has rejected that because it says it appears to offer Britain too many trading advantages without deeper negotiations which it is only willing to start after Britain has left the Union.

Yet if a deal is to be struck, the focus will be finding a formulation that makes a customs border between Northern Ireland and the British mainland highly improbable and/or makes a UK-EU future customs zone more certain than Brussels now wants. And more permanent than May's hardline Brexit supports would accept.

"There are many ways to skin a cat," another EU diplomat working on the Brexit conundrum said. "But only so many -- and we have looked at all of them. So it's either the backstop or all of the United Kingdom staying inside our customs zone."