The general election exit poll indicated that the Conservatives will be the largest party at Westminster but may not secure an overall majority. It means a deal could allow Mrs May to govern the country and win key Commons votes. For example, while the main Nationalist/Republican parties do favour marriage equality, the SDLP for example, hold exactly the same highly restrictive views on abortion as the DUP.
Birmingham MP Jess Phillips, Labour MP for Birmingham Yardley, said: "For the DUP to be holding power in Westminster is a slap in the face".
The Prime Minister will be desperate to get agreement from the DUP to back her legislative programme in the House of Commons or risk her government falling.
"But also because we think strategically that is the way to a united Ireland".
DUP leader Arlene Foster has told Sinn Fein leaders if they are concerned about her party's enhanced influence at Westminster they should move to restore devolution at Stormont.
The party only stands for election in Northern Ireland.
"People regard the peace process, which was very hard earned over very many years by a lot of people, people shouldn't regard it is a given".
There is also concern that Mrs May's planned deal with the DUP could threaten peace in Northern Ireland, as the Government could no longer claim to be impartial between the unionist community which the DUP represents and the the republican and nationalist community.
As he arrived at the Dáil in Dublin ahead of Enda Kenny's formal resignation as Taoiseach, Mr Adams said incoming Irish premier Leo Varadkar needed to put his efforts into restoring powersharing north of the border.
Alliance deputy leader Stephen Farry said the first roundtable talks in the process were not expected until Thursday at the earliest. It wasn't something people naturally chatted to me about.
He added: "We're looking forward especially to the meeting with the DUP and the DUP leader".
"We need people to step up to the plate and do so without delay".
"They talked about their kids' schools, the NHS and housing".
"But they know they won't get (an election)", Professor Cowley said.
"We're ready to go".
"I understand there is a new United Kingdom government and changes in the government in the Republic but there remains no impetus to this process, which doesn't inspire confidence", he said. Some of those same human rights violations, such as the criminalisation of a woman's right to choose whether or not to continue a pregnancy, only concern most people the rest of the United Kingdom now that they risk facing the effects of them personally under a potential DUP-Tory deal.
The irony of a Conservative/DUP alliance is strong, after a campaign in which Theresa May accused Jeremy Corbyn of links to various terrorist groups.
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