Tory Eurosceptics are threatening to torpedo a plan to give Theresa May “enormous firepower” to renegotiate her Brexit deal with the EU.

Brexiteer sources said the hardline European Research Group (ERG) could not yet support amendments put forward by senior Tories to scrap or limit the controversial Irish backstop, which would give the PM more breathing space. 

The amendments, tabled by Sir Graham Brady and Andrew Murrison, could be voted on by MPs on Tuesday, if they are selected by Commons Speaker John Bercow. Number 10 is thought to tacitly back the plans.

The idea is that a swell of Tory support for either amendment would allow May to demonstrate to Brussels that the Brexit deal could command a parliamentary majority if the EU makes concessions on the backstop.

But if ERG Brexiteers refuse to back the plans, the PM would find it much more difficult to do this.

Sir Graham said his proposals would give the prime minister a mandate to seek “legally binding” changes to the backstop which has turned many Tories against her deal. 

But a Brexiteer source said the ERG want Downing Street to say explicitly it would attempt to reopen the legally binding part of the deal – the withdrawal agreement – as a potential price for their backing.

Senior ERG MP Sir Bernard Jenkin told ITV News: “(The Brady amendment) is very vague and it’s deliberately vague because it’s meant to mean different things to different people.

“And if people vote for that in the expectation that some things are going to happen and then they don’t happen it is going to lead to more misunderstanding and disappointment, it won’t help at all.

“I will not be backing the Brady amendment as far as I have decided so far but there are discussions going on and let’s see what comes out of those discussions.” 

On Monday, May’s official spokesman said the EU would have to change the Brexit deal for it to pass the Commons,

But the spokesman was unclear on whether this would mean reopening the withdrawal agreement or adding legal “codicil” to tinker with the backstop to the deal, which may not satisfy the ERG. 

The spokesman told reporters: “We reached an agreement with the EU in relation to the withdrawal agreement and future partnership. That was put to a vote of MPs and MPs rejected that deal by 230 votes.

“The prime minister is absolutely committed to leaving the EU with a deal, but clearly if we are to obtain parliamentary support for that deal some changes are going to have to be made.”

Asked however whether the PM was now explicitly seeking to reopen the withdrawal agreement, the spokesman said: “Clearly an issue of significant concern has been the backstop, and the concerns which MPs have that it must only be temporary.

“As to how we address those concerns, that work is ongoing and we will set out any further details in due course.”

Sir Graham told BBC Radio 4’s Today programme that any alternative arrangement would have to be “legally binding” as “I don’t think anybody is going to accept something which is just warm words”.

Sir Graham said his amendment was drawn up after meetings with ministers including May.

Asked if it had Government backing he said: “I’m hoping that the way in which the amendment is crafted can attract that very broad support and if we can win the vote on my amendment then I think it gives the prime minister enormous firepower.”

European Commission spokesman Margaritis Schinas again insisted that Brussels would not reopen the withdrawal agreement.

“We have a unanimous EU27 position on the withdrawal agreement which reflects the common EU position,” he said.

“This withdrawal agreement has been agreed with the UK government, it is endorsed by leaders and is not open for renegotiation.”

Asked if that position would change if MPs vote to demand changes to the Irish backstop, Schinas said: “The only thing I have to say is that we shall wait for the result of the vote of the Commons tomorrow. 

“Then we will wait for the (UK) government to tell us what are the next steps. That’s how it’s going to work.”

Tuesday’s Commons debate will be opened by Brexit Secretary Stephen Barclay and closed by May, her spokesman said.

The day’s debate will be followed “as soon as possible” by a second meaningful vote on whatever deal has been secured with Brussels, said the spokesman. Like the meaningful vote defeated by a margin of 230 earlier this month, this will also be amendable 

It is understood that the second meaningful vote – expected to take place in February – will go ahead whether or not the EU has agreed to amend the withdrawal agreement reached with the UK in November.

May was continuing with talks with Conservative MPs and MEPs on Monday about possible amendments to her package.