But Mrs. May suffered something of a blow when a former Conservative prime minister, John Major, urged her to avoid any deal with the unionists because of the potential for destabilizing Northern Ireland and harming the Good Friday agreement, the 1998 deal that brought relative peace to Northern Ireland, especially at a moment when power-sharing in Belfast has broken down.
“The danger is that however much the government tries, they will not be seen to be impartial if they are locked into a parliamentary deal in Westminster with one of the Northern Ireland parties,” Mr. Major said.
And some of her own more liberal-minded Conservatives, like Ruth Davidson, the popular and openly gay leader of the Scottish Conservatives, are unhappy about dependence on a party that opposes abortion and gay marriage. Ms. Davidson has already sought special assurances from Mrs. May that social policy in the rest of Britain would not be altered or held hostage because of any deal with the D.U.P.
But Mrs. May has no other options if she is to have a government that provides a semblance of stability, as she has promised, with negotiations on Britain’s exit from the European Union, known as Brexit, looming as early as next week.
There was trouble building on that score, too. Her predecessor, David Cameron, who held the referendum on a British exit and quit after he lost it, used his first public comments since last Thursday’s election to urge Mrs. May to consider “a softer Brexit,” describing “an opportunity to consult more widely with the other parties on how we best can achieve it.”
While Mrs. May was correct to remain in office, Mr. Cameron said, he warned that “over Brexit, she is going to have to talk more widely, listen to other parties” — not just the Scottish Conservatives, who are eager for an exit that allows free trade, but also the opposition Labour Party.
Mrs. May will not regard those comments as helpful, and she has already said that she wants an exit that will take Britain out of the European Union’s single market and customs union. Only that way, she has argued, can Britain control immigration and make its own trade deals free of the jurisdiction of the European Court of Justice.
But in a weakened position, she has also had to retain Philip Hammond as her chancellor of the Exchequer, and Mr. Hammond has emphasized that he wants a deal that does the most to protect British jobs and trade. He would prefer that Britain at least remain in the customs union.
But that position, which seems roughly to be that of the Labour Party, is anathema to the “leave” supporters in Mrs. May’s cabinet and her own party. So here, too, she is stuck, without the obvious authority to force everyone into line.
There is a logical problem with a softer British exit, of course. To remain in the single market, Britain would have to accept freedom of movement and labor for all European Union citizens, which is exactly the issue that drove the leave campaign to victory in the referendum — to “take back control” of immigration.
The customs union is a lesser association, but it covers only free trade in goods, not services, which make up nearly 80 percent of the British economy. And even the customs union does not allow Britain to make its own trade deals with other countries in the world, as the Brexit supporters demand — it has to follow European Union trade arrangements.
What drives the other European Union member states slightly crazy is this continuing delay by Britain, which, after all, initiated the process of leaving. The referendum was a year ago. The official notice of leaving was given on March 29, meaning that Britain will be out, deal or no deal, on March 29, 2019.
The clock is ticking, but given Mrs. May’s humiliating loss of her parliamentary majority, will Britain be thrown into another national debate about what kind of exit it wants?
On Tuesday evening, Mrs. May traveled to Paris to meet Europe’s triumphant new president, Emmanuel Macron of France. The meeting centered on antiterrorism policies and concluded with both leaders watching a France-England soccer match, which England gracefully lost, 3-2.
But the real issue, of course, is Britain’s exit from the bloc. France wants to get on with it and restore its cooperative relationship with Germany as the essential dual motor of the European Union. Brexit, then, is a distraction, and while both France and Germany want to preserve good economic and military relations with Britain, the cohesion of the bloc is paramount for them.
Mrs. May said there was “a unity of purpose” in Britain on Brexit. Mr. Macron did not even raise his eyebrows. But asked in English whether there would be “open doors” in Brussels should Britain change its mind on leaving, he answered carefully and deliberately in French.
Until the negotiations end, he said, “of course there is always the possibility to reopen the door.” But once they begin — and they are scheduled to start next week — “we all should be well aware that it is much more difficult to turn back.”