The two candidates vying to be Britain's next prime minister set a high bar for success in Brexit negotiations, saying that even a significant concession from the European Union on the border would be insufficient.
Both Boris Johnson and Jeremy Hunt said that they would not be willing to accept the backstop element of Theresa May's Brexit deal, even if a time limit was set.
Britain's next leader will be announced next week and has to persuade the EU to restart talks that other EU leaders have been adamant cannot be reopened, or else lead Britain into the economic uncertainty of an unmanaged exit.
Now it is clear the winner must also persuade Brussels to drop one of its most steadfast demands, an insurance policy designed to prevent the return of a hard border between Ireland and Northern Ireland.
Asked during a leadership debate whether the backstop would be acceptable if a time limit could be agreed, both Mr Johnson and Mr Hunt said it would not.
"I'm not attracted to time limits or unilateral escape hatches or all these elaborate devices, glosses, codicils and soon that you could apply to the backstop," Mr Johnson said during a leadership debate organised by the Sun newspaper and TalkRadio.
Mr Hunt agreed, adding: "The backstop, as it is, is dead ... I don't think tweaking it with a time limit will do the trick , we've got to find a new way."
Opposition to the backstop within Britain's deeply divided parliament was one of the key reasons outgoing Prime Minister May's deal was rejected three times, losses that ultimately forced her to resign.
But a senior politician from the Democratic Unionist Party, which props up the Conservatives in parliament and opposed Mrs May's deal, said last month the party was not looking for "earth-shattering" changes to the backstop.
Eliminating a hard border between Ireland and Northern Ireland and providing frictionless trade was a crucial part of a Good Friday Agreement.
The two candidates' positions set out to go far beyond what Mrs May managed to negotiate with the EU.
The EU has said it is not prepared to renegotiate the deal, but both Mr Hunt and Mr Johnson are promising to do so, and want to take Britain out of the EU by the current deadline of 31 October.
Mr Johnson has the more hardline stance and refuses to countenance any further delay to Brexit after Mrs May's government was forced to delay it twice beyond its original date of 29 March.
When it was put to Mr Johnson that it was completely unrealistic to get the deal renegotiated and passed by 31 October, he said: "I don't think it is remotely unrealistic."
Mr Hunt said he would be prepared to delay Brexit if a deal were in sight, but that he would take Britain out of the bloc without one if it was clear no agreement could be reached.
He warned parliament not to try and block a no-deal Brexit.
"I would urge my colleagues not to take no deal off the table, I think it is one of the most dangerous and destructive things they can do when we are trying to get a deal but we can't control what parliament does," Mr Hunt said.
"The deal that is going to get through the House of Commons, the deal that is going to get us out of the EU won't have that backstop and that is what we are going to put right."