Discussions are under way over the creation of a formal alliance between the Democratic Unionist Party (DUP) and Conservatives which could end with MPs from the right-wing Unionist party installed in Cabinet positions.
Government Chief Whip Gavin Williamson has flown to Belfast to open discussions with the DUP on "how best they can provide support" for the Tories, with a Number 10 source confirming the talks would include the possibility of a formal coalition.
Coalition government must by definition include members from all parties within its executive positions, and it would be unprecedented if at least one such position was not at cabinet level. Ms May will certainly hope the DUP MPs will be satisfied with a number of the roughly 50 ministerial positions below cabinet rank.
An online petition against any Conservative deal with the controversial DUP has already reached 500,000 signatures, and protests have taken place in central London against the alliance.
Short of a full coalition agreement, Theresa May could seek a looser arrangement, known as "confidence and supply", in which the DUP would support Conservative legislation on a case by case basis. But this potentially hands the DUP greater leverage than a formal arrangement in which they were to become part of the government, as they would have the freedom almost to pick and choose between various pieces of legislation, and on Brexit, there will be many.
The party, which is deeply informed by Protestant religious views, has prevented the legalisation of same-sex marriage in Northern Ireland.
There are also fears that any deal would threaten to undermine the Good Friday agreement, the centrepiece of the Northern Ireland peace process.
Under the terms of the agreement, Unionists and Republicans are supposed to share power, with the Westminster government acting as a broker, and can step in if relations between the two groups, Sinn Fein and the Democratic Unionist Party, break down.
If the DUP were themselves part of the government, the neutral role of the UK government would be compromised.
Sinn Fein leader Gerry Adams has expressed grave doubts over the anticipated deal between the Conservatives and the DUP, in whatever form it takes.
"History will show, alliances between Ulster unionism and British unionism has always ended in tears," he said.
"It is far better to look to our own place, to all of the people here, to deal with the people of this island, this part of the island as one community."
The DUP said that no formal discussions would take place over the weekend. Leader Arlene Foster has said she will come to London on Monday to begin talks with Theresa May.
The Prime Minister has been forced into negotiations after calling a snap election with the expectation of increasing the slender parliamentary majority she inherited from David Cameron, but instead lost it altogether.
Having been twenty points ahead in the polls at the start of the campaign seven weeks ago, the Conservatives won just 318 seats, eight short of an overall majority, and dozens below even modest expectations.
Any formal deal with the DUP will attract harsh criticism. The leader of the Scottish Conservatives, Ruth Davidson, said she had been "given assurances" by the Prime Minister that no concessions would be made over LGBTI rights, an issue Ms Davidson, who is gay and engaged to be married to an Irish Catholic, said was "more important" to her than her party.
What demands the DUP might make of the Conservatives in a coalition arrangement are not clear. Government sources indicate it is likely to involve guarantees on a frictionless border between Ireland and Northern Ireland, and no further checks on travel between Northern Ireland and the UK. But these are thing that all parties involved in the Brexit negotations, including the UK and Brussels, agree on.
It is highly unlikely it will seek to impose its hardline agenda on sex marriage and abortion. These matters are already devolved to the Northern Irish Assembly at Stormont.
Tory MP Sarah Wollaston insisted any deal with the DUP must not influence social policy.
The MP for Totnes and former Health minister said: "I will always oppose the death penalty & would resign if others imposed it. They won't.
"I will always support the right for women to choose & access safe termination of pregnancy & will oppose any change to the legislation.
"I will never agree to any dilution of LGBT rights.
"Creationism in schools? Hell no.
"If any of that is a condition of confidence and supply it simply won't work."
