BRUSSELS — British Prime Minister Theresa May’s two days of efforts to persuade European leaders to soften their Brexit demands appeared to backfire Friday, as a Brussels summit broke up with Europe’s stance tougher than it was before her diplomatic push.

Facing rebellion at home over compromises she made in negotiating how Britain will withdraw from the European Union, May sought adjustments to sweeten the agreement for her Tory backbenchers and allow an orderly ­Brexit in March.

E.U. leaders initially appeared open to symbolic statements to help calm British furies. But even symbolism moved out of reach after May’s efforts unsettled Europeans who are weary of dealing with Britain’s domestic political dramas.

Several European leaders said they were directing their governments to speed emergency preparations for Britain’s crashing out of the E.U. with no deal at all, a prospect that could create a humanitarian and economic crisis after the March 29 exit deadline. And although May tried on her way out to spin the meetings as a success, her fellow leaders suggested that her statements bore little relationship to reality.

Those take us forward. Those are welcome. This is the clearest statement we’ve heard yet from the European Union that it’s their intention for the backstop never to be necessary,” May said of a Thursday night statement from the 27 other E.U. leaders that simply repeated the substance of the already agreed, toxic-in-London deal.

The backstop refers to a provision that would keep Britain in the E.U. customs union if a better solution is not found to preserve an open border between Northern Ireland, which is set to leave along with Britain, and Ireland, which will remain in the E.U. Everyone agrees they need to keep the border open to prevent a return to sectarian violence in Northern Ireland.

May said she would keep speaking with fellow leaders to win further reassurances that customs union membership would only be temporary.

But others said that while phone lines to Europe were always open, changes to the deal were impossible.

“I have no mandate to organize any further negotiations,” said European Council President Donald Tusk. “But, of course, we will stay here in Brussels, and I am always at Prime Minister Theresa May’s disposal. It’s my job and it’s my pleasure.”

He noted that, for all the criticism directed toward Europe by hardcore advocates of Brexit, “we have treated Prime Minister May with much greater empathy and respect than some British MPs, for sure.”

The Brussels spinout capped a week that started when May yanked a parliamentary vote on her Brexit deal because it was bound for spectacular failure. She then successfully faced down a rebellion from her own party — but won a confidence vote by a sufficiently small margin that she emerged badly weakened. Hours later, she flew to Brussels.

She found a stony reception from other E.U. leaders, who stripped out conciliatory language from a declaration they released after an hour of contentious back-and-forth with her.

The frustration was captured on camera Friday morning as May engaged in a tense exchange with European Commission President Jean-Claude Juncker. 

Juncker, at a news conference the night before, said that “our U.K. friends need to say what they want, rather than asking what we want,” adding that “this debate is sometimes nebulous and imprecise.”

May took it as a personal criticism. As leaders milled around before sitting down for their meetings Friday, she confronted Juncker in a rare moment of public anger. Both leaders later confirmed the tension. 

You called me nebulous,” May appeared to say in the video, which had no audio. May later characterized the conversation as “robust.”

“We were not dancing,” Juncker told reporters afterward. “I did not refer to her but the overall state of the debate in Britain.”

He added that they had already made amends, as diplomats do. “During the course of the morning, having checked what I said yesterday night, she was kissing me,” he said.

May’s domestic opponents, smelling blood, seized on the skepticism.

“The last 24 hours have shown that Theresa May’s Brexit deal is dead in the water,” opposition Labour Party leader Jeremy Corbyn tweeted. “She’s failed to deliver any meaningful changes. Rather than ploughing ahead and recklessly running down the clock, she needs to put her deal to a vote next week so Parliament can take back control.”

European leaders said they had heard no new proposal from May that they believed could actually shift the debate in Britain while adhering to their already-negotiated agreement. And several said the assurances they offered in Thursday’s declaration — which May said were a starting point — were in fact their final offer.

“The signals we got yesterday are not particularly reassuring,” said Belgian Prime Minister Charles Michel. He said he was directing his government to prepare for a no-deal Brexit.

“The 27 member states have given assurances that are contained in the conclusions of yesterday,” German Chancellor Angela Merkel told reporters. “That is what we have put on the table and now we expect Great Britain to respond. We are all preparing for the eventuality of a disorderly Brexit, which is something we will be working hard to prevent from happening.”

May must now return to fighting domestic battles before mounting an attempt to pass the deal through Britain’s Parliament before the end of January. Few European diplomats believed Friday that she would succeed.