The counterattack is thought to be being led by Brexit Secretary Dominic Raab and Foreign Secretary Jeremy Hunt along with the support of 12 other Cabinet ministers.
They will be delivering their demands during today’s weekly Cabinet meeting.
They will demand Mrs May get a mechanism added to the EU deal that would allow for the UK to decide how long it remains in a backstop customs union so that they can keep the Irish border open.
If she fails to get the mechanism in place, then the Conservative leader risks having any deal signed with Brussels torpedoed by nearly 40 Tory backbenchers in the House of Commons.
According to the Sun, Chief Whip Juilan Smith has told the Prime Minister the Government could only rely on 15 Labour MPs voting in favour of a deal rather than the 40 that have been previously claimed.
A Cabinet minister told the Sun: “We must have control of the backstop.
“If Theresa doesn’t stare down the EU and win a mechanism that does this, the whole argument is immaterial as there is zero chance of passing the Commons.
“She just doesn’t have the numbers.”
Another Cabinet source said: “It’s important for us to be able to say we really have taken back control and been true to the referendum result.”
The meeting comes as some inside No 10 claim a no deal scenario is becoming increasingly likely and an emergency EU summit being pushed back until the end of the month.
The Irish Premier Leo Varadkar also added to tensions by saying he would never agree to give the UK “unilateral” power to decide when to pull out of the backstop.
Following this statement, Mrs May called the Taoiseach and offered to add a “review mechanism”, a compromise he said he was considering.
However, he added that unless both sides agree on when to pull the trigger or else the backstop “isn’t worth the paper it’s written on”.
Mr Varadkar said he was hoping to see a Brexit deal signed by the end of the year.
While HM Revenue and Customs (HMRC) officials have said they will use two new inland spots as a way to inspect suspicious freights in the hopes it will relieve some pressure on ports if there is no deal, HMRC chief on Thompson said: “The time to implement an optimal No Deal system has gone.”