Critics accuse Jeremy Hunt and Boris Johnson of making empty promises — already rejected by the EU — that will send the U.K. crashing out of the 28-nation bloc without a deal to cushion the shock.
Many Brexit-backing lawmakers reject it because it would keep Britain bound to EU trade rules in order to maintain an open border. And Northern Ireland's Democratic Unionist Party, which props up the U.K.'s minority Conservative government, opposes the backstop over fears it could weaken the bonds between Northern Ireland and the rest of the U.K.
EU leaders insist that without the backstop there can be no withdrawal agreement.
Hunt told Conservative Party members in Belfast that "we are never going to have a deal to leave the EU with the backstop. So it has to change or it has to go."
He said a "technology-led solution" could remove the need for customs posts and other border infrastructure. Britain and the EU have agreed to look into technological fixes, but say a solution doesn't currently exist.
Johnson said "the withdrawal agreement as it currently stands is a dead letter."
He called the backstop a form of "moral blackmail" by the EU, and later tweeted: "I will never accept a deal that seeks to bind us in the EU's customs union forever, or which divides our United Kingdom."
Three years on from Britain's 52%-48% vote to leave the EU, Britain's departure has been delayed twice by the country's political impasse. It is currently scheduled for Oct. 31, and both Johnson and Hunt say they will lead the U.K. out of the bloc, with or without a divorce deal.
Most economists say leaving without an agreement would severely disrupt trade between Britain and the EU, plunging the country into recession.
But Johnson said the warnings had been "wildly overdone."
"We should not be terrified of a no-deal Brexit," he said.
Johnson and Hunt are competing for the votes of about 160,000 Conservative Party members across the U.K. The winner, to be announced July 23, will replace May as party leader and prime minister.
The new leader will face a country, and Parliament, deeply divided over Brexit.
Polls suggest most members of the Conservative Party support a no-deal Brexit, and shrug off the warnings of economic turmoil. But most Britons, and the bulk of British businesses, oppose the idea.
Treasury chief Philip Hammond, who has made increasingly loud warnings to Conservative colleagues about the risks of a no-deal Brexit, said Tuesday that leaving the EU without a divorce agreement would mean a 90 billion pound ($114 billion) hit to the public purse.
"It would be wrong to pursue 'no deal' as a policy, and I believe it will be for the (House of) Commons, of which I will continue proudly to be a member, to ensure that doesn't happen," Hammond told lawmakers.
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