Having survived a no-confidence challenge from her own MPs in Westminster on Wednesday, the prime minister had a bruising night in Brussels where her plea for meaningful changes to the Brexit deal was rejected by European Union leaders.
The prime minister admitted she had a "robust" discussion with Jean-Claude Juncker, captured by the cameras as leaders sat down for private talks.
She also said he had been talking about "the general level of debate" when he used the term "nebulous".
The EU agreed they should try to ensure the backstop was never needed by swiftly working to reach a new trade agreement with the United Kingdom after it has left, and to find alternative arrangements as soon as possible if it was activated.
He added: "We don't want the United Kingdom to think there can be any form of renegotiation, that is crystal clear".
'But my discussions with colleagues today have shown that further clarification and discussion following the council's conclusions is in fact possible.
Mr Tusk added: "We have treated Prime Minister May with the greatest respect, all of us".
But she said that it was clear that "further clarification and discusssion" is possible. But her contemporaries in Europe echoed similar sentiments of Juncker who made it clear that "there is no room whatsoever for renegotiation".
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Pichai said worries about harmful uses of AI are "very legitimate" but that the industry should be trusted to regulate its use. Besides the Chinese problem, Pichai was asked if Google had rigged its search algorithm to favor certain political parties.
Asked three times whether the United Kingdom could get further concessions or legally binding assurances that go beyond the current agreement, the German chancellor, Angela Merkel, declined to suggest another offer would be forthcoming.
Liam Fox, the worldwide trade minister, said Thursday the Cabinet could block May from bringing her exit withdrawal deal before the House of Commons next month and that it might insist Britain's scheduled departure date of March 29 be moved back several months to provide time for a fresh approach.
Brussels would like London to set out its expectations on the withdrawal within a few weeks, Juncker added.
'Our UK friends need to say what they want, instead of asking us to say what we want, ' he said.
Mrs May managed a smile at her press conference when a reporter asked if she had had a "trying week", jokingly replying: 'Has something happened this week?' "Something that people do in the real world all the time, but which seems so alien in our political culture - to engage with others", she said.
Under huge pressure at home as British media described her largely unsuccessful plea for favour from European Union leaders as a humiliation, May appeared anxious to make a point to Juncker before a new session in the morning.
"Negotiations like this are always tough", May said. "There are always hard times and as you get closer to the very end, that can get even more hard because you are sorting out the last details of something".
Labour leader Jeremy Corbyn said: "The last 24 hours have confirmed that Theresa May's Brexit deal is dead in the water".