PM and Arlene Foster hold crucial talks on deal to back Tories
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.
Mrs May's authority has been severely diminished after a disastrous general election which saw her lose her Commons majority and a deal with the DUP looks vital for the continuation of Tory rule.
A failure to gain support from the Northern Irish party would risk the Queen's Speech being voted down next week, and Jeremy Corbyn has said Labour will be pushing hard for that outcome.
The Tories and the DUP are considering a "confidence and supply" arrangement which would see the Northern Irish party back the Government to get its Budget through and on confidence motions.
It comes after Mrs May told Tory MPs: "I'm the person who got us into this mess and I'm the one who will get us out of it."
Her most senior minister Damian Green has confirmed the Queen's Speech setting out the Government's programme could be delayed if a deal is not reached in time for it to go ahead on Monday as planned.
The PM told the backbench 1922 Committee on Monday that a deal with the DUP would not affect power-sharing talks in Northern Ireland or LGBT rights.
Mrs Foster has also rejected suggestions that the mooted agreement could undermine a return to power-sharing arrangements at Stormont amid claims from political rivals that the Government's stated impartiality as a mediator would be fatally undermined.
The DUP leader declined to give details of what she termed a "positive engagement with the Conservative Party", but said she would be travelling to London late on Monday for discussions with her team of 10 MPs before a meeting with Mrs May at Downing Street on Tuesday.
Sinn Fein's Gerry Adams turned Mrs May's own slogan against her to brand it "a coalition of chaos", adding: "Any deal which undercuts in any way the process here or the Good Friday Agreement is one which has to be opposed."
It is thought Mrs Foster, despite being a Brexit supporter, could seek assurances from Mrs May that she will pursue a softer exit from the EU, given Northern Ireland's 56% Remain vote and the DUP's desire not to see a return to a hard border with Ireland.
The DUP leader is almost certain to ask for greater investment in Northern Ireland as the price of a deal.
Any demands on maintaining the pensions triple-lock and the universal winter fuel allowance could give Mrs May a convenient excuse to drop manifesto pledges which appeared to be deeply unpopular with voters.
Movement on security and legacy issues from the Troubles may prove more difficult for Mrs Foster to extract from the Government.
The unexpected snap election has already forced the Queen to cancel an Order of the Garter service and to accept a stripped-down State Opening of Parliament.
Any further delay could mean her missing planned attendance at Royal Ascot.
Additional delay may be caused by the fact the Queen's Speech is written on goatskin parchment paper, which requires several days for the ink to dry.
The paper does not contain any goatskin but is high-quality archival paper guaranteed to last for at least 500 years.
Pen cannot be put to paper until the exact contents of the speech are finalised, which appears to be dependent on the outcome of Tory talks with the DUP.
While Mrs May appears to have seen off the threat of an immediate leadership challenge, her weakened grip on power has put her under pressure on several fronts.
Her new chief of staff Gavin Barwell has suggested she should take a different approach towards public spending after Labour unexpectedly denied the Tories a majority after running an anti-austerity election campaign.
The PM also faced calls from Scottish Conservatives leader Ruth Davidson, whose influence has grown dramatically with the election of 13 Tories north of the border, to pursue a softer Brexit with greater focus on the economy and more cross-party input.
In another sign of Mrs May's weakening grip on power, MPs who attended the 1922 Committee revealed she was open to more backbench input on policy and a greater role for Chief Whip Gavin Williamson.
New Environment Secretary Michael Gove has insisted he backs the Prime Minister despite the election result, saying she has "amazing gifts and incredible talents".
Asked how long he would support the woman who sacked him less than a year ago, he told Good Morning Britain: "For as long as she wants to be Prime Minister."
Mr Gove, a staunch Brexit supporter, was also asked about a Daily Telegraph report that senior Cabinet ministers were engaged in secret talks with Labour MPs to secure a soft Brexit.
Despite writing a column for the same edition of the paper, the former journalist said it was "news to me", adding that the story may have involved a "slight amount of top spin".
Mr Gove insisted Mrs May was "resolute and determined" to set out plans for the next five years.
He told Sky News: "The Prime Minister spoke with, I thought, great authority and also she was generous in acknowledging that the result was not what it should be.
"She was generous in acknowledging how sad we naturally felt that some of our colleagues had lost their seats and that was as a result of this election campaign being called at the time it was called.
"But she was also resolute and determined in plotting a path over the course of the next five years which will ensure the country emerges stronger and which will ensure that we not only strengthen the economy but also invest more in public services and make sure the quality of people's lives is enhanced."
Mr Gove, who last year brought Boris Johnson's leadership bid to an end, said it was "wonderful to be sitting alongside" the Foreign Secretary in Cabinet.
He said: "It was great to have the chance to chat to Boris over the course of the weekend.
"I've been talking to Boris regularly over the course of the last year", he added.
Asked about the DUP's stance on austerity as a deal is discussed, Mr Gove said: "We don't have a majority, and one of things which I do think we need to do is to make sure that, when we bring forward a programme, it can command the broadest possible level of public confidence, and we also need to reflect on what the election result told us about the way that people want to see the economy managed in the future and I think that there is an important balance to be struck.
"We need to get on with the job of reducing the deficit so that we do not saddle the next generation with the burden of debt, and the larger the deficit the more money that should be spent on health and education is actually spent on paying down debt."
Mr Gove told BBC Radio 4's Today programme that there was a need to ensure public spending was kept at a level and in a way that was sustainable but stressed that "we also need to take account of legitimate public concerns about ensuring that we properly fund public services in the future".