Savaged by both Remainers and Brexiteers, the PM is desperately trying to drum up support for her Brexit blueprint and keep it on the negotiating table.
In their final exchanges before the parliamentary summer recess, the Labour leader said she was neglecting the country's needs because she was caught up in Tory infighting.
"We've only got 12 weeks really left to nail down the details of the agreement, so I set out our proposals", Raab said after meeting Barnier.
As ever, the main sticking point remains how to avoid a "hard border" between Northern Ireland and the Republic.
Britain and the European Union have agreed on a transition deal bridging Brexit in March next year and the end of 2020, but it has yet to be ratified, meaning financial firms based in Britain could face an abrupt end to European Union market access.
'I've also been clear we will not accept the imposition of any border down the Irish Sea and we will preserve the integrity of the UK's internal market and Northern Ireland's place within it'.
"The only thing that could replace this current form of a backstop is, No. 1 something which is better; No. 2 something which is agreed and No. 3 something that would be legally operable", Finance Minister Paschal Donohoe told RTE radio.
The plan makes clear the United Kingdom is unwilling to accept European Court of Justice (ECJ) jurisdiction and will end freedom of movement.
The Irish Prime Minister (taoiseach) Leo Varadkar has previously said the agreement must be fully reached by the October summit.
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Mrs May said: "We continue to do all we can to see the re-establishment of devolution and all of the institutions of the Belfast Agreement".
During the week, the House of Commons passed a motion that would prevent Northern Ireland agreeing to have separate custom arrangements to the rest of the UK.
"Article 50 requires, as we negotiate the withdrawal agreement, that there's a future framework for our new relationship going forward, so the two are linked", Raab said.
However, during her visit to Belfast, Mrs May will reiterate that a hard border is not acceptable.
The Sinn Féin leader also said Theresa May's speech "showed scant regard for the Good Friday Agreement, scant regard for the democratic will of people in the north who voted remain and absolute disregard for people's rights and entitlements" and added that it "might have been written by a member of the DUP".
Mr Donohoe also said he believes that Mrs May's commitment to an open border is genuine and honest.
Mr Barnier is expected to make a statement around 13.00 after a meeting of European Union ministers, giving reactions to the UK's "white paper" on its ideas for the future relationship.
The 500-kilometre (300 mile) border has been largely invisible since army checkpoints were taken down after a 1998 peace deal ended three decades of violence between the region's pro-British majority and an Irish nationalist minority. "We just haven't finalised the wording of it yet", Irish Foreign Minister Simon Coveney told RTE radio.
Speaking to the BBC, Raab refused to deny reports the government is planning to stockpile food or use a section of motorway in England as a lorry park to deal with increased border checks if Britain leaves the European Union without a deal.