Can Theresa May survive the next seven days?

A week is a long time in politics, they say, but the old cliche now has a particular resonance for Theresa May.

The Prime Minister "is now officially on the clock", says Vox. "If she can't strike a deal to maintain power in the next week or so, her government will fall apart."

However, before May can shore up her minority government, she is in Brussels, "battered and bruised," says Politico.

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Today's summit, which comes almost a year after the referendum, is May's first encounter with all EU leaders since the general election.

European diplomats said their leaders were keen for the PM's update on the state of the government, amid uncertainty about whether the Tories will manage to strike a confidence and supply agreement with the Democratic Unionist Party (DUP).

A deal with the Northern Irish party will be May's next task after Brussels - together with consolidating support within her own party, heading off a potential challenge by Labour leader Jeremy Corbyn and attempting to pass her government's agenda in the crucial Queen's Speech vote on June 29, all while her reputation is in tatters.

Following the general election, "May's reputation crashed, arguably faster than any other in modern British political times", says the BBC's Laura Kuenssberg.

"It humbled her, weakened her, leaving May a 'wounded antelope' in the words of one of her senior colleagues."

Lessons learned

"Theresa May has survived because the Conservatives have applied the lessons of last summer, or perhaps of the Iraq war: toppling a leader is easy but the ensuing tribal warfare is the killer," writes Fraser Nelson, editor of The Spectator.

Martha Gill in The Guardian agrees. "[May] is here to soak up bad feeling after the election, which stirred anger about Tory austerity, and to absorb as much blame for Brexit missteps as possible," she says, adding that one party member told her: "There is quite a big caucus in the party who hope they can keep her until the Brexit negotiations are over.

"Brexit will be a car crash – she can be blamed for that."

DUP deal

Jeffrey Donaldson, the DUP's chief whip at Westminster, told journalists the prospects of a the party striking a deal with May were "very good" - "the sooner the better as far as we're concerned," he added.

But BBC Northern Ireland reports that in exchange for giving the PM their support, the Unionists want £1bn for the health service in the province and another £1bn for infrastructure projects.

The Daily Telegraph warns the deal could end up costing UK taxpayers even more under the Barnett formula. "Typically £1 spent in the Province would require an additional £35 to be found for Scotland, England and Wales," it says.

The Queen's Speech

Conservative MPs insist they are "sufficiently confident" they will be able to get the Queen's Speech through the House of Commons.

"It would be hard for a unionist party to be responsible for toppling the government and paving the way for a Labour government under Jeremy Corbyn, who met with members of the IRA during the 1980s," says Politico.

But even if May does win the vote with the help of the DUP, that doesn't mean she's safe, says the New Statesman's Stephen Bush.

Under the Fixed Term Parliaments Act, only the votes on the Queen's Speech and the Budget are classed as votes of confidence, he says, after that "the government can lose any number of votes – over the legislative timetable, over Brexit, over its core programme as set out in the Queen's Speech – and it won't fall".

This, argues the journalist, gives the DUP the upper hand. "They will be able to hold the government up by voting with it on the Queen's Speech and the budget – but they will be free to let them down any time on anything else."

The Opposition threat

The Telegraph has also reported that Labour, the Liberal Democrats and the Scottish National Party could introduce amendments during the vote on the Queen's Speech to force a vote of no confidence in May's government.

According to Catherine Haddon, resident historian at the Institute for Government, the "political reality" is that May would be under enormous political pressure to resign or would face an immediate vote of no confidence from Labour if the Queen's Speech is defeated.

The Good Friday Agreement

Should Theresa May stagger on, there are potentially even more serious consequences in the months ahead, both politically and legally, because the Good Friday Agreement demands political neutrality from the UK government regarding power-sharing in Northern Ireland.

A legal team with experience making constitutional challenges is preparing a judicial review in anticipation of a pact with the DUP being announced, says The Guardian.

If the challenge is lodged, High Court judges would be asked to consider whether the government would be in breach of its commitment to exercise "rigorous impartiality" as part of the historic peace deal.