The Prime Minister’s statement in Downing Street this morning presented three central arguments against MPs voting that they have no confidence in her leadership.

Unfortunately, each of the three suffers from some fundamental flaws:

1. “A new leader wouldn’t be in place by the 21st of January legal deadline”

There are two reasons to think that this simply isn’t correct.

For a start, the House of Commons itself has publicly stated that the deadline is no longer 21st January, but 28th March. And, it must be said, that just because May has said she would abide by a January deadline, that doesn’t mean she actually would – she said she would hold a vote on her deal this week, but she hasn’t, so evidently her diary is flexible. Either way, it’s a soft ‘deadline’ at best.

Also, there is no good reason why even a contested leadership election couldn’t take place swiftly even if May’s claimed deadline was correct. The timetable for the process is set by the 1922 Committee, in consultation with the Party Board, and they have the power to accelerate or delay the timetable as they see fit. The ’22 has already acted swiftly in holding the confidence ballot today, apparently to the dismay of some MPs who hoped they would have more time, which shows they are willing and able. What’s more, the Conservative Party has recently centralised all of its membership databases, so it would be quicker than last time (2005) to hold a ballot of members, too – potentially including some use of online voting, as in the London Mayoral selection contest.

2. “The new leader wouldn’t have time to renegotiate a withdrawal agreement…so one of their first acts would have to be extending or rescinding Article 50”

The blunt fact is that her negotiation – and now her renegotiation of her negotiation – is dead. It’s dubious as to whether she is really in any position to tell others what they can or cannot achieve, given her analysis of the process has foundered so badly.

On the question of “extending or rescinding Article 50”, this peculiar threat goes back to a question we have asked repeatedly of the Government, but which has yet to be answered. May has promised she would do no such thing, and that the UK “will leave…on 29th March 2019”. No other Conservative minister or potential leader has said they would do any such thing either – and it is hard to see any leadership candidate being elected on such a promise. And yet those around her – and now the Prime Minister herself – keep predicting that an alternative Conservative government “would” delay or cancel Brexit. If they wouldn’t do it themselves, and the alternatives say they wouldn’t either, whom is it that they are claiming would?

3. “A leadership election would not change…the parliamentary arithmetic”

This is obviously true, in its most basic sense. But it is not a reason to keep the Prime Minister in office. She has lost, fatally, under that parliamentary arithmetic – that is why she was not even able to put her proposals to a vote in the House of Commons yesterday. There is no sign of her being able to remedy that failure, or to present a convincing case of how she might try to do so. Yes, a different Prime Minister would face the same arithmetic, but they would at least have the opportunity to seek to manage it differently, from a fresh start.

If this is Downing Street’s best case for May to hold on, it is not a very convincing one. It was also notable, watching her at that podium, that there wasn’t really much of an attempt to make a positive argument for continuing her premiership – the unifying theme of the three arguments above is merely that the alternative wouldn’t work, so we might as well carry on as we are. That seems unlikely to light a fire in many hearts.