It comes after an estimated 700,000 protesters marched through London on Saturday demanding a “People’s Vote” on the terms of a deal, and a wave of speculation in the Sunday newspapers that a vote of no confidence in the prime minister could be imminent.
But in an article for The Sun newspaper, Mrs May plays down the personal pressures she faces, writing that “the Brexit talks are not about me or my personal fortunes. They’re about the national interest”.
She goes on to acknowledge “the very last stages of the talks are going to be the hardest of all”.
“Does that mean I think the negotiation will get tougher before we reach our goal? Yes,” she adds.
“Do I have some long and difficult days ahead? I’m sure I do.”
“But what I’m thinking about is not how hard it all is today. I’m thinking about the prize that lies before us tomorrow,” she concludes.
On Monday afternoon she will also deliver a statement to the Commons where she is expected to set out the progress that has been made so far in the Brexit negotiations.
In addition to referencing the agreement on citizens’ rights, the Brexit divorce bill and the transition period, she will cite further developments in the last three weeks, including:
:: A memorandum with the Spanish government on the future of Gibraltar,
:: A protocol with Cyprus relating to military UK sovereign base areas in the country,
:: “Broad agreement” on security, transport and services in the “structure and scope of the future relationship”.
But Mrs May will also acknowledge there remains a fundamental dispute over how to avoid a hard border between Northern Ireland and the Republic of Ireland.
The prime minister will say the UK government’s commitment to avoiding a hard border has already been “enshrined in law” as part of the EU Withdrawal Act, but that EU demands for a backstop that would leave Northern Ireland in the customs union and single market risked “breaking up the integrity of the UK”.
“I do not believe that any UK prime minister could ever accept this. And I certainly will not,” she will say.
The so-called Irish backstop is the commitment agreed last December that the UK will maintain alignment with EU rules “unless and until” a future trade agreement is in place that can maintain a frictionless border.
The EU’s legal interpretation of that commitment, which will form part of the final Withdrawal Agreement, is that Northern Ireland alone would need to remain in the customs union and parts of the single market.
The UK government has proposed an alternative UK-wide backstop, known as the “temporary customs arrangement”, but ministers insist it must be time-limited or have a clear exit mechanism.
At last week’s summit of EU leaders in Brussels, Mrs May said the UK would be prepared to consider an extension of the “implementation period”, which is currently due to end in December 2020, if this reduced the chance a backstop would be needed.
Speaking to the BBC’s Andrew Marr on Sunday, Brexit Secretary Dominic Raab said any extension of that transition phase would also need to be time-limited, suggesting it should be “three months or so” and would require a clear exit clause to avoid “any sense that we are left indefinitely in a sort of customs union limbo”.
Meanwhile, a group of senior Brexiteers who oppose the prime minister’s strategy are set to meet the EU’s chief negotiator, Michel Barnier, in Brussels.
Former Northern Ireland secretary Owen Paterson, former Conservative leader Iain Duncan Smith and former first minister of Northern Ireland Lord Trimble will be joined by Hans Maessen, former president of the Dutch customs association, and Shanker Singham, from the Institute of Economic Affairs.
It is understood the group will present Mr Barnier with the findings of a report produced by the European Research Group, a hard Brexit wing of Conservative MPs, which was published in September.
The report rejected the prime minister’s preferred “Chequers” model of maintaining a common rule book on goods with the EU, and the UK collecting tariffs on behalf of the EU, in favour of a looser free trade agreement, like that which exists between Canada and the EU.
The group is expected to argue concerns over customs infrastructure at the Irish border and risks to the Good Friday Agreement could be overcome with technological solutions.