Instead, her spokeswoman said only that it must be “temporary”, a much looser word that – pro-Brexit MPs fear – will leave the UK locked into an effective customs union for many years to come.
The clash came after The Independent revealed that Andrea Leadsom, the Commons leader, is prepared to resign if the compromise is made, with other cabinet ministers believed to be ready to follow her.
Esther McVey, the work and pensions secretary, Penny Mordaunt, the international development secretary, and even Liam Fox, the international trade secretary, are also on “resignation watch”.
Underlining Ms May’s dilemma, the Irish government described any attempt to put a time limit on the backstop as a “deal-breaker” – insisting it would never risk the “corrosive impact of a physical border re-emerging”.
Simon Coveney, Ireland’s deputy prime minister, also predicted a deal on the backstop would not be reached at next week’s crucial EU summit because the UK’s proposals were not ready.
Meanwhile, the Democratic Unionist Party (DUP), which is propping up the Conservatives in power, stepped up its pressure on Ms May by urging her to show EU negotiators the door.
The row over the customs backstop burst out into the open when the prime minister’s spokeswoman was asked if the reworked proposals, being negotiated in Brussels, would have “an end date” and be “time-limited”.
A June paper stated it should be “time-limited”, but the spokeswoman repeatedly refused to use the word, saying only that “the arrangement would be temporary”.
She attempted to head off a backlash by adding: “The prime minister would never agree to a deal which would trap the UK in a backstop permanently.”
The spokeswoman also insisted the UK would insist that a replacement for the backstop “needs to be in place by the end of December 2021 at the latest”.
However, without a legal requirement for that to happen, written into the Brexit withdrawal deal, it would depend on the EU agreeing later that as-yet-unproven technology has produced a solution.
If it refused, the Irish backstop would then lock the entire UK permanently into an effective customs union, unable to sign its own trade deals, many Tories fear.
A few hours later, Mr Raab directly challenged No 10, saying: “It would have to be finite, it would have to be short and it would have to be, I think, time-limited in order for it to be supported here.
“What we cannot do is see the UK locked in via the backdoor to a customs union arrangement which would leave us in an indefinite limbo. That would not be leaving the EU.”
Downing Street insisted there was no divergence, arguing “temporary” effectively meant “time-limited”, but Brexiteers view the absence of an end date as crucial.
One said: “Income tax was introduced as a temporary measure to meet the cost of the Napoleonic wars, yet it’s still with us.”
No 10 also did not deny a report that the Brexit negotiations were exploring a possible extension of the transition period – under which the UK is due to abide by EU rules until the end of 2020.
Such a plan would be designed to convince the DUP to agree to the backstop on the grounds that it will never come into force.
The government is also believed to be pushing for a “review clause” that could bring an end to the backstop, but its legal strength is unclear.
The dropping of an end date was attacked by Steve Baker, a leading Brexiteer Tory, who said it risked “effectively committing the UK to membership of the single market and customs union”.
“That won’t wash. The British people voted to take back control over money, laws borders and trade,” the former Brexit minister said.
And Nigel Dodds, the DUP’s deputy leader, said the U-turn would be “unacceptable”, tweeting: “On many occasions both the PM and the Brexit secretary said the backstop would be time-limited. This is critical.”
He also hinted at further clashes, saying: “I think there could be developments over the weekend in terms of the government’s own position and the cabinet.”
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.