As the Conservative Party digested the loss of its majority in last week's election, government officials suggested both the announcement of the prime minister's agenda, known as the Queen's Speech, and talks over Britain's divorce from the European Union could be postponed.
Less than a week before Brexit talks are due to begin, Ms May faces conflicting demands within her own party and even a proposal for business groups and politicians from all parties to agree on a national position for Britain's most complex negotiations since World War II.
In an article for the Times on Tuesday, the new Environment Secretary Michael Gove - who has clashed with May in the past - said she was the ideal person to secure a Brexit agreement that "commanded the widest possible support" given her track record of "seeing through vital jobs to the end".
"It won't surprise anyone that we are talking about matters that pertain of course to the nation generally, bringing stability to the United Kingdom government in and around issues around Brexit, obviously around counter-terrorism, and then doing what is right for Northern Ireland in respect of economic matters".
"Hopefully we can make a bit more progress later on Tuesday", he said.
Brexit minister David Davis on Monday insisted that the government still aimed to take Britain out of the European Union single market.
Meanwhile, the chief European Union negotiator has told the Financial Times that the clock is ticking on Brexit talks, and that Britain should be wary of further delays. "I can't negotiate with myself", Barnier was quoted as saying by the Financial Times.
"Going overseas and being seen to be the prime minister and talking to the president of France... is a classic move to shore up authority at home", said Colin Talbot, professor of government at the University of Manchester.
May tried to reassert her shattered authority at the weekend by announcing her new cabinet - with no changes among her top team.
May also restored former Justice Secretary Michael Gove to the Cabinet in another move created to show she was willing to listen to critics.More news: Ask SAM: When did Flag Day start?
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Mrs May was attempting to thrash out a pact with Mrs Foster at a meeting in Downing Street to prevent the collapse of her administration.
As Mrs Foster met with her MPs in Westminster, she said: "The future's bright", prompting Ian Paisley junior to respond: "The future's orange".
The Irish republican Sinn Fein party which won seven seats in the election although MPs traditionally do not take up their seats in protest is also wary of the alliance.
Earlier, Foster said the talks were going well: "We hope soon to be able to bring this work to a successful conclusion". "I am dubious about it", Major said.
The Conservatives and the Democratic Unionists are expected to announce a deal that would see the DUP supporting a Tory-led minority government.
He stressed he did not share their ultra-conservative views on issues such as abortion and homosexuality, which have caused disquiet among many Conservatives.
As he arrived at the Dail 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.