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Theresa May has set a date for what's probably her last attempt to pass a Brexit deal - and she's told Labour there's an urgent need to compromise.

The odds of her succeeding are faint - and her time's nearly up.

There's every risk Mrs May will fail, again, to deliver Brexit when she introduces her Brexit legislation in the first week of June.

This will come after what look like being tough European elections and, by the way, during the week of President Trump's official visit to the UK.

Tonight, she also told Jeremy Corbyn time was running out to reach any deal with Labour. But the reality is there has been no breakthrough in those talks, and no obvious reason to expect one.

A cross-party agreement which involved Labour's minimum demand of a customs arrangement with the EU would cause a mutiny among Tory MPs, as Tuesday's letter to the Times newspaper warns vividly.

It would also mean a revolt among Labour MPs if there's no guarantee of a new referendum, and Mr Corbyn has shown very little enthusiasm for that.

Meanwhile, Mrs May's under quite intense pressure. Her most senior MPs, the executive members of the 1922 committee, will press her this week for a timetable to step down.

Local Tory officials will gather in June and consider passing a humiliating vote of no confidence in her. And in the European elections, the polls are looking very promising for Nigel Farage's Brexit Party.

So promising that Mrs May's last, best, hope may be that the elections shocks both big parties into backing her.

And if that sounds like clutching at straws, well, Mrs May's in a corner, all but out of time, and reaching and clutching at any hope she can find in what are now the dying days of her premiership.