It came as Mrs May's "inner cabinet" was briefed last night on plans for a no-deal Brexit amid reports that progress ahead of a crucial European Union summit next week had been slower than hoped.
While London wants to regulate that by a future trade deal with the European Union, the bloc insists on an emergency fix in case negotiating new relations takes longer, or fails.
"If the prime minister were to cave in to the demands that we know Michel Barnier is making. that's serious enough, for the United Kingdom, for us to take the kind of action that we're going to take, and that we have threatened to take".
The news comes after the Democratic Unionist Party threatened to vote against the Budget, and potentially bring down the Government, in opposition to a backstop plan that would treat Northern Ireland differently to the rest of Great Britain.
"They [the EU] said they think this is an unbelievable deal you are getting, something nobody else in the world has even been offered", said Seamus Leheny, the director of policy at the Freight Transport Association of Northern Ireland, who was at the meeting.
The DUP vehemently opposes any checks between Northern Ireland and mainland Britain after Brexit, which is due in March and would be the United Kingdom's biggest trade and foreign policy shift for more than four decades.
Barnier told small business leaders that the talks were "continuing intensively this week, day and night, with the aim. of having a deal within reach, if we follow through to the end of this negotiations, on October 17".
Speaking to reporters in Brussels, Margaritis Schinas said: "We are not there yet". Britain's Brexit minister, Dominic Raab, could also come to Brussels then if weekend talks cover enough ground.
If the DUP votes against the budget, which will be presented on October 29, this could trigger a confidence motion and a general election if the government loses.
Mrs May is to brief key ministers on negotiations with the European Union later.
Earlier today the DUP leader was not prepared to discuss last night's "warning shot" in the Commons, when her MPs didn't back the government in a parliamentary vote.
In a Q&A session with Reuters, Tony Blair advised parliamentarians to vote the Brexit deal down.
But he stuck to the EU's rejection of London's plan for a "regulatory framework for goods", saying it would give Britain an unfair competitive advantage by allowing access to parts of the bloc's single market without ensuring the country honours all of its conditions.