The Prime Minister is thought to be considering improving the divorce bill offer, after European diplomats told her £18billion (€20bn) will not be enough.
And sources close to the British negotiating team said talks are at risk of collapsing if Brussels refuses to take a more reasonable approach.
But Eurosceptics in the Conservative party said the divorce bill settlement is “critical” – and the UK cannot afford to concede even more ground.
Former Tory leader Iain Duncan Smith told the Telegraph: “They think we blinked in Florence and now they believe we will blink again. We must not blink.
“The one big hand we have is money. They are desperate. If we give away that, we give away any chance of getting a good free trade agreement.
“The two get decided at the same time. The money is critical, we cannot give any more ground on this. Tory Eurosceptics are getting really unnerved by this.
“It is stretching them to breaking.”