Theresa May’s plan to bring her Brexit deal back to parliament for a vote at the start of June has generated weary indifference at Westminster and beyond. In many ways it is, of course, easy to see why. Her Brexit deal was defeated in January, and then twice more in March. The deal hasn’t changed much. Her own authority is vestigial. So what is the point of trying for a fourth time, or of treating the attempt seriously?

The parliamentary arithmetic hasn’t altered since the last failure. Talks with Labour have been and gone. The mood in Brussels is hardening against the UK. The Tory party, meanwhile, is expecting another electoral kicking and is increasingly obsessed with the succession, as is the media. Is it any wonder that both are acting as if Mrs May’s government no longer exists?

There is a hard core of unavoidable truth here. Mrs May’s deal is a bad one because it is so dangerously vague about the future. That has not changed. There is no majority for most Brexit outcomes and options in the current parliament. That hasn’t changed either. And Mrs May is being levered out of office by the hard Brexiters who tried to oust her in December and who are now having another go. Nothing new there, then.

But there is also an enormous amount of magical thinking mixed up in what is happening. The Tory right is engaged in a deceitful and self-deceiving bluff that is full of danger for the country. It talks as if a different leader would secure a different and harder Brexit deal that would carry in the Commons and be so popular in the country that the Tories would win a substantial majority in an early election. Yet there is no evidence whatever to support any part of this argument. It is as unimpressive as Jacob Rees-Mogg’s new book appears to be.

A new leader would not get a new deal out of the EU. Neither the public nor the House of Commons supports a hard Brexit, let alone an even harder no-deal one. The public in general has cooled on Brexit. The Tory party’s ratings are falling in the face of Brexit’s failure. Even if there was an early election (which is itself not straightforward), the chances of it producing another hung parliament are high. The rightwing narrative is sloppy and wishful thinking. Above all, it is wrong.

This is not to say that Mrs May’s latest plan stands much chance – let alone that it should. She has squandered too much political capital for that. The moment for such initiatives has probably passed. Nevertheless, this could be a more serious opening than it has been given credit for being. It may not be the “new, bold offer” that Mrs May claimed at the weekend – the details have to get through cabinet this week, which suggests it will be thin stuff. But it is a recognition that the previous strategy of one-off votes on the 2018 EU-UK deal has run out of road.

Instead, the government is now planning to bring forward a withdrawal agreement bill. This allows the government to try to sweeten the original pill by including, on the face of the bill itself, what the international development secretary Rory Stewart yesterday called “extra guarantees” on some of the issues on which the Tory-Labour talks were focused, such as employment rights and the environmental crisis. If nothing else, this means the bill is less likely to be blocked by the Speaker.

Bills are amendable, so it is conceivable that alliances may form to make additional changes. Mrs May offers “votes in parliament to test support for possible solutions”, though this has not worked in the past. She will also have to win on the second reading, before any amendments can be made, which Labour and many Tories may not be willing to allow. But there are issues – from customs arrangements to a confirmatory referendum – on which the government could give assurances and the Commons express views that could perhaps tip the vote their way.

The odds seem slim on Mrs May snatching any sort of victory from the jaws of defeat before she is chased off into retirement. Yet the attempt to pass a bill is an important moment. Without some kind of convergence next month, it seems unlikely that Brexit can be resolved in the current parliament. But that does not make it any more likely that it can be resolved in the next parliament either.