With the negotiations coming to a head, the central focus of the discussions is thought to have been the issue of the Northern Ireland "backstop" meant to ensure there is not return of a "hard border" with the Republic.
"The principle, and our red line, is that the whole of the United Kingdom is treated the same".
"Many of her cabinet colleagues have assured me of their unionism", she said.
DUP leader Arlene Foster said that any border effectively being drawn in the Irish Sea between Northern Ireland and Britain would be "catastrophic".
The discussion is expected to include a commitment to keep the whole of the United Kingdom in an effective customs union with the EU after Brexit, but with a "clear process" of steps to exit.
The DUP has 10 MPs, although Ian Paisley will not be able to vote in the Commons until November 20 after being suspended for failing to declare two family holidays paid for by the Sri Lankan government.
Technical talks are continuing at official level in Brussels this week, but no visit by Brexit Secretary Dominic Raab has been announced, and Downing Street would say only that new proposals on the border issue would be released "in due course".
"So it is in both the Party's interest, and crucially the national interest, that we reset our negotiating strategy immediately and deliver a Brexit that meets the demands of the referendum and the interests of the British people".
Barnier is still set to brief the meeting on Brexit talks, but is unlikely to seek approval for a formal text, according to European Union sources who spoke to Irish broadcaster RTE.
She has come under growing pressure from Brexit-backing Tories to drop the plan agreed by the Cabinet at her country residence in July and instead seek a Canada-style free trade deal.
Theresa May is used to presenting the European Union with her red lines for a Brexit deal, but now it's the prime minister who is being challenged to meet tough conditions by her DUP partners.
If Ms May secures a deal with the European Union, she has to get the British parliament to approve it and would need the backing of about 320 lawmakers to get approval.
The former chancellor said that would reveal the "hardline Eurosceptic views" of the "Bennites" in the Labour leadership and the "right-wing nationalists" on the Tory benches were in the minority in the Commons.
"The Prime Minister is doing an exceptional job and everybody is behind her", he told reporters.
An announcement on what a possible deal could look like on the Irish border issue could be made as soon as Monday.
International Development Secretary Penny Mordaunt, who campaigned for Leave in the referendum, said Mrs May "has my support and I am not in any way expecting that situation to change".