British Prime Minister Theresa May framed her "new" offer to MPs as "one last chance" to deliver Brexit.

But, more accurately, it likely will be May's last chance.

She has signalled she will step down if her thrice-rejected divorce deal fails again in the House of Commons, as it is widely expected to do.

In a sign that the British public has already moved on, many of the questions May fielded during today's news conference had to do with when she will resign and what might happen after that.

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Parliament is scheduled to vote again on the Brexit deal she negotiated with the European Union during the first week of June - which, coincidentally, is also when US President Donald Trump will be making a state visit to Britain.

"What I'm doing today is setting out what I believe is a new Brexit deal that can command a majority in the House of Commons," said May, a fatally wounded but dogged politician.

Offering a binding vote on a second referendum, as well as on whether Britain should remain in a temporary customs union with the EU, represents a shift in strategy for May.

She said she recognised "the genuine and sincere strength of feeling" on the referendum issue. But she also reiterated her long held views that a second referendum was not her preferred way out of the current Brexit impasse. Extending the Brexit debate, she said, "risked opening the door to a nightmare future of permanently polarised politics."

May hopes that with those additional voting opportunities and some tweaks to her deal - including pledges on environmental protections and workers' rights - she can win over enough MPs to get it over the line. But early indicators were not looking good.

Some Conservative MPs who'd previously backed May said they would now oppose her. The Scottish National Party and ChangeUK said they would not back her. Nigel Dodds, the deputy leader of Northern Ireland Democratic Unionist Party, which props up May's Conservatives, said the proposal had "fundamental flaws."

The opposition Labour Party has been internally divided on whether to push for a second referendum, with leader Jeremy Corbyn reluctant to embrace the idea.

In a speech that was at times reflective, May said she never thought delivering Brexit would be "simple or straightforward," but said it had "proved even harder than I anticipated". She said that she'd given it her all, even offering to "give up the job I love earlier than I would like".

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In the question-and-answer session that followed her speech, May was asked several times about her departure and who she'd like to see replace her. May didn't offer fresh details, but she has previously promised to outline the timetable of her departure if she loses the next Brexit vote.

The unofficial race to replace her is underway. Today Jacob Rees-Mogg, an influential Brexiteer, threw support behind former foreign secretary Boris Johnson, who is leading the polls.