However, putting the pro-British unionist DUP in a position of influence in London could also undermine the British government's ability, enshrined in a 1998 peace agreement, to function as an impartial broker between Northern Ireland's unionists and its Catholic Irish nationalists.
"We will be asking the prime minister to be open with politicians and also with the public", he said.
But May faces a hard balancing act: Divisions over Europe helped sink the premierships of Margaret Thatcher, John Major and David Cameron, and many of her lawmakers and party membership support a sharp break with the EU.
Arlene Foster, leader of the DUP, has rejected claims that her party is homophobic. During the election campaign, May had used the "coalition of chaos" phrase to describe what a victory for Labour would look like.
With negotiation dates now up in the air and the United Kingdom government desperately attempting to stabilize, it will be interesting to see how the European Union reacts.
"I'm the person who got us into this mess and I'm the one who will get us out of it", she said. The meeting is taking place to see if an alliance can be created to push through the Conservative Party's agenda after a disastrous snap election left her short of a majority in Parliament.
"That being said a sovereign decision was taken by the British people and that is to come out of the European Union and I very much respect the decisions taken by the people, be it by the French people or the British people", he noted.
On Tuesday afternoon, Foster indicated that a deal was close to being finalised.
Brexit minister David Davis has insisted the approach to the European Union divorce had not changed, but at the meeting with lawmakers on Monday, May recognized that a broader consensus needed to be built for Brexit and made clear she would listen to all wings of the party on the issue.
"Any deal which undercuts in any way the process here or the Good Friday Agreement is one which has to be opposed", he said.
Sinn Fein's Stormont leader, Michelle O'Neill, said she would raise the issue with the Prime Minister in face-to-face talks in London on Thursday.
The stakes for May are high.
Labour leader Jeremy Corbyn is pushing for this outcome, and has repeatedly said he was ready to try to form a government.
Theresa May should agree to pay Britain's bills to the European Union and drop threats to walk out without a legal deal if she wants talks on the "softer Brexit" some of her allies are calling for, EU negotiators say.
Speaking in an interview with various European publications, Michel Barnier warned that time is "passing quicker than anyone believes - because the subjects we need to deal with are extraordinarily complex from a technical, judicial and financial point of view".