Theresa May has said she is prepared to “explore every possible option” to break the deadlock in Brexit talks.
She told MPs 95% of the terms of exit were agreed but the Irish border was still a “considerable sticking point”.
While willing to consider extending the transition period beyond 2020, she said this was “not desirable” and would have to end “well before” summer 2022.
Labour’s Jeremy Corbyn said the Tories were “terminally incompetent and hamstrung by their own divisions”.
The UK is due to leave the EU on 29 March 2019.
Many Conservative MPs are unhappy about plans floated at last week’s EU summit for the transition period after the UK leaves next March to be extended beyond the end of 2020.
Both Brexiteers and Remainers worry it would delay further the moment of the UK’s proper departure from the EU, and potentially cost billions in terms of extra payments.
The PM has not ruled out the idea, which its backers say would give the two sides more time to agree their future economic partnership and ensure that controversial contingency plans to avoid a hard border on the island of Ireland, the so-called backstop, do not ever come into force.
Mrs May told Monday’s edition of The Sun that protecting the UK’s integrity was so important that she had a duty to explore “every possible solution” to keeping the Irish border open and ensuring no new barriers within the UK as a whole.
“Does that mean I think this negotiation will get tougher before we reach our goal? Yes.” she wrote.
“What I’m thinking about is not how hard it all is today. I’m thinking about the prize that lies before us tomorrow; about the great opportunities the government will help open up for you once we clear the last few hurdles.”
She suggested the talks should not be personalised and her own future was secondary compared to getting a deal which respected the 2016 Brexit vote but also protected jobs.
“The Brexit talks are not about me or my personal fortunes,” she added. “They’re about the national interest – and that means making the right choices, not the easy ones.”
A weekend of feverish speculation suggested Mrs May had 72 hours to save her job ahead of a meeting of the 1922 committee of backbench MPs on Wednesday.
One of those who has called for a vote of confidence in the prime minister, backbencher Andrea Jenkyns, said she feared the PM was playing for time.
A leadership contest can be triggered either if the leader resigns or if 15% of MPs – that is currently 48 – write to the chair of the 1922 Committee, demanding a vote of no confidence.
Emerging from his meeting with Mr Barnier, Mr Duncan Smith said the PM had his “full support, full stop” and suggested anyone using aggressive language against her should be disciplined.
He denied he was undermining the prime minister by making the case for a deal with the EU which did not require the UK to sign up wholesale to its rules for trade in goods, as her plan envisages.
“We are presenting some ideas which we think are constructive. We had a constructive discussion and now we are going to talk to the government about it.”
In her statement, Mrs May will cite the agreement reached in the last few weeks on the future of Gibraltar and the UK’s RAF bases in Cyprus as sign of the progress that is being made.
“Taking all of this together, 95% of the Withdrawal Agreement and its protocols are now settled.”
In advance of Mrs May’s statement, ministers fielded urgent questions from MPs about the cost to the UK of extending the transition period and the terms of the “meaningful vote” the Commons has been promised on Brexit.
Ex-Conservative cabinet minister John Redwood said staying in the EU’s customs union up to the end of 2021 could cost the UK between £15bn and £20bn at a time when resources were “desperately needed” for domestic priorities such as the NHS, schools and Universal Credit.
He told MPs it would be “an act of great rashness” to a financial settlement which amounted to a “surrender document which we cannot afford”.
Treasury Minister John Glen said there was “no expectation” that the UK would be paying any extra money on top of the £39bn already committed to in the event of a negotiated exit but the “length and cost” of any transition period would be subject to the negotiating process.
Brexit Secretary Dominic Raab said the motion for the Commons vote on the deal would be amendable, subject to the discretion of the Speaker, but this could not be allowed to prevent or delay the UK’s departure from the EU.
The choice MPs faced, he said, was between the “best deal” negotiated by the government and a no-deal alternative, adding he was “very sure that will focus minds”.
But Labour said it would not support this while former Tory education secretary Nicky Morgan questioned what legal advice ministers had received to support its position.