BRUSSELS — British Prime Minister Theresa May traveled Thursday to Brussels to beg fellow E.U. leaders for concessions in her effort to seal a divorce deal splitting her nation from the European Union, but won little to sway opinions among her rebellious supporters.

In a series of one-on-one meetings and a nearly hour-long grilling by the E.U. leaders, May underlined the direness of her predicament, as an exit deal that could leave Britain stuck partway out the door of the European Union has proven too politically toxic to pass muster at home. But some blasted May for what they said was the muddiness of her proposals, and it seemed possible the exchange could actually inflame the British discussion rather than calming it. 

One leader, European Commission President Jean-Claude Juncker, said the British demands were “nebulous and imprecise.” In a declaration following their meeting, the 27 leaders said the deal “was not open for renegotiation” and directed all levels of their governments to prepare for “all possible outcomes” — including a chaotic British departure that could set off a European economic crisis. 

“There’s an impression perhaps in the U.K. that it’s for the E.U. to propose solutions,” Juncker said. “It is the U.K. that is leaving the E.U., and I would have thought it was up to the British government to tell us what they want.” 

Other leaders were softer on May and appeared to be trying to give her political cover in her domestic drama, but they still made clear that no changes to the divorce deal would be possible. 

“Each side should play its part,” German Chancellor Angela Merkel told reporters as she left the meeting. “That means us, but we also ask Britain to come up with good suggestions” to make the deal politically palatable in the British parliament. 

May pressed fellow leaders for assistance. 

Britain's Prime Minister Theresa May secured enough support from members of her Conservative Party to win a no-confidence vote on Dec. 12. (Sarah Parnass/The Washington Post)

“There is a majority in my parliament who want to leave with a deal,” May told leaders in their closed-door meeting, according to a spokesman. “With the right assurances, this deal can be passed. Indeed, it is the only deal that is capable of getting through my parliament.” 

The Europeans said they were willing to entertain any proposal, so long as it was not exactly what many British rebels are seeking: reassurances, with legal weight, that Britain would not be locked permanently into a sort of junior-class E.U. membership, subject to many of its rules but unable to sway its decision-making. 

Still, leaders tried to make clear to British lawmakers that they had little interest in keeping them bound to the European Union forever. 

“There is absolutely no argument for anyone, both the U.K. side or on the European Union side, to keep that limbo state any longer than is absolutely necessary. That is the key message from tonight,” said Dutch Prime Minister Mark Rutte. 

The controversy has already cost May her own political future. She promised Wednesday that she would step down ahead of the next British elections, in 2022, in exchange for support in a confidence vote that nearly toppled her. She may yet go into history as the leader who presides over a chaotic exit from the European Union that throws up borders overnight and throws both Britain and its European neighbors into economic crisis. 

She pleaded with fellow leaders to try to avoid that possibility. 

“It is in none of our interests to run the risk of accidental ‘no deal’ with all the disruption that would bring,” she said. 

Leaders said Thursday that they wanted to do everything they could to avoid that happening, but that they could offer little leeway on the basics of the deal. Some diplomats said they were confused about what precisely May was asking for. 

Other European countries, watching the political chaos engulf Britain, are stepping up emergency preparations in case Britain crashes out of the union on March 29 without a deal in place. Diplomats say they believe that is increasingly likely, since the British Parliament appears paralyzed by fragmentation. Although May won Wednesday’s confidence vote, the 200-to-117 party vote exposed the depth of anger within the Tory ranks and left it unclear whether any Brexit deal proposed by the unpopular leader can carry the parliament.

If there is no deal, planes won’t be able to fly between Britain and mainland Europe. Transportation would grind to a halt, and food and medicine from Europe would no longer flow into Britain. Millions of Europeans living in Britain and British living in the E.U. could lose their legal status overnight. The economic toll could throw Britain into a depression. 

Although Europeans say they may be able to put in place temporary emergency plans to offset some of the pain, they would far prefer a deal. Negotiations could be extended with the consent of the remaining 27 E.U. leaders, but E.U. diplomats say that would only happen if negotiators were confident that the extension was in the service of wrapping up the current deal, not beginning a new one. And late June is probably the latest they could go, given Europe’s election calendar. 

Many leaders made clear they were exasperated by the back-and-forth British debate, where members of May’s own cabinet have demanded changes to a deal they approved just last month. 

Lithuanian President Dalia Grybauskaite tweeted a photograph of a chocolate Christmas tree and told the British: “Finally decide what you really want and Santa will deliver.” 

Austrian Chancellor Sebastian Kurz, asked what Europe could offer to help the deal pass in Britain, said the debate there had slipped away from reality. 

“It is difficult to judge,” he said, “because many of the skeptics do not really argue rationally.” 

According to the deal on the table, if the two sides cannot strike an acceptable trade agreement before the end of Britain’s two-year transition period, Britain would remain inside the E.U. Customs Union. The primary concern is to avoid a hard border between Ireland, which is staying in the E.U., and Northern Ireland, which would depart along with the rest of the United Kingdom. Both sides fear a revival of the decades-long Northern Irish conflict if border infrastructure goes up. But staying in the customs union would prevent Britain from striking many trade deals, and it would also keep it bound to E.U. regulations with no power to shape them.

May is seeking to limit how long Britain could be stuck inside the backup plan. 

Leaders, after meeting late into Thursday night, offered the same assurances they made ahead of time: they will do everything they can to avoid triggering the backup plan embedded inside the divorce agreement. But they said they cannot offer Britain an escape clause, as hard-line pro-Brexit lawmakers have demanded. 

If anything, the uncertainty over May’s future hardened resolve among E.U. leaders that they need ironclad guarantees for the future relationship between Britain and the rest of the European Union, since they cannot rely solely on assurances from a leader who may not last much longer on the job.