May is seeking a loose "confidence and supply" arrangement with the DUP's 10 MPs that would allow her to press ahead with a minority government, after losing her Commons majority in general election. Conservative MPs are publicly airing their anger, some calling for her ouster and others demanding radical change in her style of leadership.
"One piece of good news is the whole election has put pay to a hard Brexit", Osborne told CNN.
Labour gained 30 seats in the general election to take its total to 262 seats, but the Conservatives remain the largest party in Parliament with 318 seats.
Asked Sunday if she is now just a caretaker leader, May noted that "I said during the election campaign that if elected I would intend to serve a full term".
"The taoiseach (Kenny) indicated his concern that nothing should happen to put the Good Friday Agreement at risk and the challenge that this agreement will bring", an Irish government spokesman said.
"She's got to form a consensus", legislator Anna Soubry, a former minister who wanted to keep the United Kingdom in the European Union, told the BBC.
The Conservatives have been forced to clarify that they are still negotiating with Northern Ireland's Democratic Unionist Party (DUP) after the party announced that an agreement had already been reached "in error".
On Sunday, May appointed former BBC journalist Damien Green as First Secretary of State - effectively May's deputy Prime Minister - in a reshuffle of her cabinet.
The Conservatives won the biggest share of seats in Thursday's election, but lost their majority in Parliament and will have to rely on support from a smaller party to govern.
A Conservative source said the move to include Gove in her cabinet may suggest she has learnt a lesson after firing George Osborne, the former finance minister who as editor of London's Evening Standard newspaper, has become a vocal critic.
"Theresa May is dead woman walking".
The DUP did not yet agree to a deal with May's Conservatives, according to Sky News, contradicting earlier reports. "There's an bad lot of issues around Brexit that need to be discussed with other parties", she told Sky News on Saturday. This is the time for us to come together as a party", culture minister Karen Bradley told Sky News.But Soubry said May's time in the top job would be limited."I just can't see how she can continue in any long-term way.
In Northern Ireland as well, this potential settlement between the Conservatives and the DUP will result in a strong affiliation between the two parties and this heightened DUP influence could prove troublesome for power-sharing negotiations at Stormont as the Conservative party will no longer be able to act as an unbiased arbitrator.
Downing Street says it hopes to finalize the deal next week, after Parliament resumes sitting.
A spokesman for Mr Johnson said: "The Foreign Secretary is 100% supporting the PM and working with her to get the best deal for Britain".
Even if a deal is struck, May could struggle to get backing from parliament for her Brexit stance.Defence Secretary Michael Fallon told the BBC the government would be able to muster parliamentary support for its Brexit plans, adding: "Our view of Brexit I don't think has changed."But Anna Soubry, a Conservative member of parliament who campaigned ahead of last year's referendum for Britain to stay in the European Union, disagreed."I don't think she does have a majority in the House of Commons for leaving the single market", she told Sky News.In a measure of the desperation in Conservative ranks, Brady, who is chairman of the influential 1922 committee of Conservative lawmakers, suggested the party could end up relying on support from pro-Brexit opposition members of parliament."We will happily have the support of members of the Labour Party as well on some of our policies", he said. They want to see government providing that certainty and stability", she said".
In another sign of the dangers facing Mrs May, Sunday papers reported that Boris Johnson was either being encouraged to make a leadership bid in an effort to oust her, or actually preparing one - a claim dismissed as "tripe" by the foreign secretary.
But Graham Brady, who chairs the influential 1922 Committee of backbench Conservative lawmakers, said a "self-indulgent" party leadership campaign would only cause more uncertainty.
"We will happily have the support of members of the Labour Party as well on some of our policies", he said.
"I am going to be backing her, and absolutely everybody I'm talking to is going to be backing her too", said Johnson, who had been touted as a possible successor to May.