Although the DUP are unionists - wanting to remain part of the United Kingdom - and broadly support numerous policies of the Conservative and Unionist Party (as the Conservatives are correctly called), May's proposed deal could scupper attempt to broker a power-sharing deal with Sinn Fein - which promotes the unification of Ireland - on the Northern Ireland Executive.
Conservative Party sources say May wants to show her government is up and running but her loss of authority in last week's election will make it harder to handle a hectic agenda - Brexit talks with the European Union, tackling a slowing economy, a political crisis in Ireland, and a devastating fire in London.
May is holding talks Thursday with other Northern Ireland political parties amid warnings the expected DUP deal will undermine the peace process.
In an unexpected move, Mr Macron said that the European Union "door remains open, always open [to Britain], until the Brexit negotiations come to an end".
"I can't negotiate with myself", was Michel Barnier's response, who's the EU's chief Brexit negotiator.
The Prime Minister's comments came after predecessor Sir John Major warned that an alliance with the DUP at Westminster risked undermining the impartiality of the UK Government as attempts were made to restore the powersharing administration in Stormont.
"However, while talks are ongoing it is important that the Government gets on with its business and we are confident there will be sufficient support across the House for passing a Queen's Speech".
Ministers have already said that the Queen's Speech, scheduled for 19 June, may have to be delayed because of the ongoing talks.
Theresa May insisted the Government was "absolutely steadfast" in its commitment to the Northern Irish peace process as she faced questions on whether a DUP-Tory alliance would put fragile agreements at risk.
"And if that wasn't enough, calling an unnecessary general election purely for the self interest of the Conservative Party and having mucked that campaign up they are now putting the country in hock to the DUP".
DUP leader Arlene Foster, who was asked to resign in the wake of a heating incentive scandal that cost the government hundreds of thousands of pounds, said on Twitter that discussions are "going well" and that there will be an agreement of sorts.
May is due to meet the leaders of all five Northern Ireland political parties, June 15, in an effort to try and form a consensus over power-sharing, following the fallout between Sinn Fein and the DUP in January, when Sinn Fein's Martin McGuinness resigned as deputy First Minister, throwing the executive - the devolved government - into chaos.
"We're united Irelanders, we want to govern ourselves".