It comes after the Prime Minister apologised to her MPs for the election result, telling them: “I got us into this mess and I will get us out of it.”
The first move in Mrs May’s new reality of compromise politics is to listen to what the DUP hope to gain by offering the Conservatives their support.
It is thought the Prime Minister is preparing to ditch unpopular policies such as her social care reforms and plans to means test the winter fuel allowance.
Arlene Foster said her party wants to “support the national interest” and “bring stability to the nation”.
She told Sky News: “We enter these talks in a positive fashion, we are first and foremost unionists and therefore we want to secure the union.
“But we do want to do so in the national interest to give stability to the Government and that’s why we will be entering these negotiations.”
Mrs May will also hold her second Cabinet meeting in two days. One senior Conservative source told Sky that “a head of steam” was building for a “softer Brexit”, with “significant people” pushing, but said the PM is “still unconvinced”.
Tory MP Sarah Wollaston told Sky News: “The reality of having a different arithmetic is that we are going to have a different kind of Brexit negotiation because at the end of it this will come back to Parliament, and Parliament will be voting on it, and that’s the same for domestic legislation as well, there is going to have to be a much more consensual approach.”
She added: “What the public want to see now is rather than the parties using this as an excuse to constantly be sniping, what the public will judge all politicians on is how prepared are we to work together in the national interest.”
Mrs May will later travel to Paris to meet French President Emmanuel Macron to discuss online radicalisation.
He and other EU leaders are no doubt keen to know where her problems have left the Brexit negotiations.
Eurosceptic Conservative MP John Redwood said: “We’re going to make a great offer to Europe in terms of their access to us and continued presence of their citizens here in Britain – they are very welcome.
“So we are very, very positive, and I hope that Her Majesty’s Loyal Opposition on this issue – when our Prime Minister is in Brussels arguing for the whole country – that they understand they said they wanted the same things and that’s what she’s trying to deliver.”
Mrs May appears to have bought some time with her MPs in her meeting with them on Monday night – most emerged impressed with what she had to say.