LONDON — Though she admits disliking the social side of politics, Prime Minister Theresa May hosted lawmakers at a party in Downing Street this week, hoping to salvage her much-maligned plans for Britain’s departure from the European Union, or Brexit.
But despite wine, canapés and what one guest called a “very pleasant social occasion,” Mrs. May brings her deal to Parliament on Wednesday knowing that she faces virtually certain defeat in a vote next week — one that could mean weeks of perilous political brinkmanship for Britain.
Mrs. May postponed the vote last month, calculating that she would lose, yet has little to show for the delay. More than two and a half years after Britons opted to leave the European Union, a divided country is still wrestling with the implications of that referendum decision and, as ever with Brexit, the answers seem to lie just over the horizon.
“We won’t get to the endgame until one or other of the options for Brexit are eliminated,” said Charles Grant, director of the Center of European Reform, a research institute, “and maybe not until March.”
On Wednesday, lawmakers passed an amendment that aims to limit Mrs. May’s ability to play for time, by obliging her to return quickly to Parliament if she loses the vote next week. She would have to explain her plans for proceeding, and lawmakers could submit their own alternatives.
It was the second defeat in two days for Mrs. May. On Tuesday, lawmakers voted for a measure designed to make it harder for the government to leave without any deal.
But, with the clock ticking and Parliament divided, the question is whether British lawmakers can agree on anything to avoid that. If not, perhaps Mrs. May will have another shot with her little-loved deal, even if lawmakers reject it as expected next week.
“At the moment it seems highly unlikely that Mrs. May can get her deal through,” said Mr. Grant. “But if the cliff edge is looming, there is no general election, a second referendum seems impossible and Parliament doesn’t want a no deal, then Mrs. May’s deal does have a chance.”
Prospects of a second Brexit referendum are rising, gaining support among members of the Labour Party. But there are practical problems, and the idea has so far been resisted by the Labour leader, Jeremy Corbyn, a lifelong critic of the European Union.
An alternative plan to keep Britain tied closely to the bloc economically, like Norway, has failed to gain traction.
While there is growing talk of Britain requesting a delay to its departure date, that would solve little unless the country also finds a new strategy.
So Mrs. May’s hope is that, if Parliament remains divided, she might use the fear of a disorderly Brexit to squeeze her deal through, perhaps after winning some last-minute concessions from Brussels.
Amid fraying tempers, the increasingly ugly mood was underscored on Monday when a TV interview outside Parliament with the pro-European Conservative lawmaker Anna Soubry was interrupted by pro-Brexit protesters shouting “Nazi.”
Inside Parliament, pro-Brexit lawmakers are furious about the agreement’s Irish “backstop” provision, which would keep the United Kingdom in a European customs union until a trade agreement with the bloc could remove the need for border checks.
Having got nowhere with that demand, Mrs. May is seeking a guarantee that a trade deal with the bloc — that would supersede the backstop — would be complete by a specified date.
But this idea has only drawn attention to one of the flaws of Mrs. May’s plan, which fudges the issue of how closely tied economically Britain should remain to the European Union.
“If the British knew what they wanted and had a unified position, then perhaps you could do that negotiation in two years,” said Mr. Grant. “But do they want a customs union? Do they want Norway? That’s one reason the E.U. would be bonkers to put a time limit on reaching a trade agreement.”
Another problem is that no one can really guarantee agreeing to a negotiation that has not even begun. “The European Union could come up with a draft agreement, but they can’t commit themselves to signing — or to the British signing — an agreement by a certain date,” said Peter Holmes, a specialist in European economic issues at the University of Sussex.
European leaders are reluctant to offer Mrs. May significant concessions if they do not think they will satisfy Britain’s Parliament. So any big changes are likely to be delayed until after the vote next week — perhaps quite a bit later — and to depend on whether they are judged likely to work.
While it is true that the European side is also anxious to avoid a disorderly rupture, Mr. Grant is highly skeptical that it will bend.
“I have no reason to think that the European Union is going to give anything of substance to Theresa May,” he said. “They think no deal will be such a catastrophe for Britain that it will at the end opt for something rather than risk it.”
Mr. Holmes, too, thinks that a disorderly exit will be severely damaging for Britain and is dismissive of the idea of a “managed no deal,” a notion championed by some pro-Brexit hard-liners.
“The European Union is going to put some arrangements in place that would mitigate some of the consequences of it, but they are not going to go out of their way to help Britain,” he said.
“The best guesses are that there would be an absolutely gigantic holdup of goods in both directions,” added Mr. Holmes, referring to trade across the English Channel.
“There is bound to be serious chaos in the short term. The real question is, does it pile up and get worse?”
Yet until lawmakers actually look over the cliff edge and decide which is their least worst option, uncertainty will remain. The problem is especially acute for British businesses, which are growing more anxious by the day.
“Running the clock down is very dangerous,” said Mr. Grant, “but what else can Mrs. May do?”