Theresa May has received a Brexit boost as the head of the influential 1922 Committee of backbench Tories signalled support for her stance.
Sir Graham Brady indicated he could swing behind the Prime Minister’s Withdrawal Agreement ahead of crunch Commons votes as he expressed optimism about a breakthrough over the Northern Ireland backstop.
Writing in the Mail on Sunday, Sir Graham said: "The whole country is tired of vacillation and delay.
"When the right compromise is offered, we should pull together behind the Prime Minister and help her to deliver our exit from the European Union on March 29."
Many Brexiteers have expressed opposition to the backstop as it would leave the UK obeying EU customs rules if no wider trade deal is agreed after a transition period.
Sir Graham, who branded the Government’s handling of the Brexit negotiations as "lions led by donkeys", indicated there was a growing mood for a deal in the Commons.
Mr Brady said: "This is not a time to make the best the enemy of the good, and most MPs are in a mood to compromise, but the danger of this backstop becoming permanent is a real one and it has to be tackled.
"My conversations with senior diplomats and politicians from across Europe have given me cause for optimism that a breakthrough is near.
"Those who have pressed for delay or for no-deal to be taken off the table have weakened Theresa May’s hand and made a deal less likely, but I still believe a compromise is fundamentally in our interest and that of the EU."
"We know what is needed to shift the logjam. The Attorney General needs to give a legally binding guarantee that the backstop is temporary.
"Once we have that, my colleagues in Parliament need to recognise the strength of feeling."
The comments came as the Sunday Times reported that the hardline European Research Group (ERG) of Tory MPs led by Jacob Rees-Mogg has drawn up "three tests" the Government must pass to win backing.
In private talks with Attorney General Geoffrey Cox, the ERG called for a legally binding mechanism to escape the backstop, with a clear exit route and an unambiguous rewrite of the language in the Government’s legal advice, the newspaper said.
The stance has been drawn up in conjunction with the DUP, according to the Sunday Times.
The manoeuvring follows Mrs May telling MPs the Commons will have a "meaningful vote" on her Brexit plans by March 12.
The PM said that if her deal is rejected, MPs will be able to vote on whether the UK can leave the EU in a no-deal scenario, and if that is rejected, the Commons can decide on whether to extend Article 50 and delay Brexit.
Meanwhile, EU chief Brexit negotiator Michel Barnier said he does not believe the UK will have enough time to approve Mrs May’s withdrawal deal by the scheduled exit date of March 29.
Mr Barnier suggested a "technical extension" of up to two months may be needed.
Asked if he thought it was possible to reach an agreement by March 29, even if Westminster gave the green light this month, Mr Barnier told Spain’s El Mundo newspaper: "No."
Mr Barnier has also stated Brussels is ready to give the UK further "guarantees, assurances and clarifications" that the Irish backstop should only be temporary.