In politics, support for televised debates comes from two sources: the broadcasters and the worried. The broadcasters, of course, have a vested interest in securing a set-piece event to burnish their schedules. Among politicians, TV debates are prized for their ability to reset public perceptions.

That’s why the 2010 general election campaign saw the first genuine debates between the party leaders, after years of pleading by the major channels. All three leaders were worried about the forthcoming election; all three thought that a live discussion was a gamble worth taking.

For Gordon Brown’s Labour, trailing badly in the polls, it was an opportunity to reintroduce their candidate to a hostile public. David Cameron, knowing that his party faced an uphill struggle to win a parliamentary majority, hoped to break the deadlock with a bravura performance. Nick Clegg, knowing that the Liberal Democrats always struggle to avoid being squeezed during close elections, hoped that the debates would keep his party in the spotlight.

In the end, only Clegg got what he wanted (remember “I agree with Nick”?), but once the debate format was established, it was hard for the parties to avoid it in future. Televised debates were a central feature of the elections of 2015 and 2017. On each occasion, the major supporters of both debates were the broadcasters and the desperate. In 2015, Ed Miliband hoped in vain that the debates would allow him to reset his public image as a geek. (“Am I tough enough? Hell yes,” he told Jeremy Paxman.)

In 2017, Jeremy Corbyn attempted the same gambit with rather more success, transforming his personal ratings and slashing a double-digit Conservative lead. He was helped by Theresa May’s decision to skip the debates; the political damage she suffered in that contest by looking evasive was obvious. Now May wants a televised debate on the withdrawal agreement she has negotiated with the European Union.

The Prime Minister may have achieved a political first: a televised debate that is almost unwanted by the broadcasters. The suggested slot of 9 December, just ahead of the Commons vote, would cut across their big TV franchises, from Doctor Who to I’m a Celebrity, Get Me Out of Here!, at a time when – in the absence of an election or a referendum – public interest in politics will be at a relative low.

Yet space can be found for the debate for the same reason that Corbyn has agreed to participate: the hope that signing up to a televised debate now makes it more likely there will be one at the next election.

The Labour leader will need a TV debate for the same reason he wanted one last time. After a brief turnaround during the 2017 election campaign, Corbyn’s personal ratings are back to their dire pre-election position. Talk to almost anyone in the inner circle and you will hear the same explanation. Corbyn is popular when he can speak without the filter of a hostile media, and unpopular when he is trapped within the confines of Westminster.

The project’s few pessimists have a different theory: that the antipathy that voters had towards Corbyn in early 2017 was based on their lack of knowledge about him, and his genial demeanour on the campaign trail won them over. However, his unpopularity now is founded in his hesitant response to the poisoning of Sergei Skripal and his handling of the party’s anti-Semitism crisis. Neither of those will be easily expunged by a good debate performance.

For the Prime Minister, calling for a televised debate has two advantages. The first is that while Westminster types are talking about TV debates, they aren’t talking about how far she is from being able to command enough votes in the Commons to get the withdrawal agreement passed. The declared opponents of the deal now comprise more than half of the Conservative back benches. (Privately, Downing Street feels that a 100-vote defeat would make bringing the deal back to the House politically impossible.)

Parliamentary rebellions tend to shrink when the moment of truth approaches, but that is partly because MPs don’t like making enemies of the whips for no reason. But here, success is guaranteed and insubordination will make them popular with their party’s grass-roots. So the rebellion is likely to snowball rather than collapse. One MP summed up the mood by texting me a quote from the Elizabethan writer John Harington: “Treason never prospers, for if it prospers, none dare call it treason.”

Under these circumstances, Theresa May very firmly falls into the category of “worried”, if not “desperate”. Her hope is that any debate will serve two purposes. First, it will generate public support for the accord, reassuring nervous Conservative MPs in marginal constituencies that they can vote in favour of it. The second is that she can generate a mood of partisan fervour around the deal by painting it as a Tory vs Labour battle, making it harder for Brexiteer ultras to vote it down.

Unfortunately for the Prime Minister, she is not an effective enough performer to do the first and no amount of Corbyn-bashing will convince the most committed Brexiteers or the DUP to vote for the accord. To pass it she will need Labour votes – not just for the withdrawal act but to enshrine the exit deal into law. And May cannot hope to encourage Labour MPs to rebel, or the party leadership to change its line, by increasing the level of political rancour around the withdrawal agreement. She can only do it by finding a way to reach out to her nominal opponents on the Labour side.

May’s decision to skip the 2017 TV debates might have contributed to the loss of her parliamentary majority and her current predicament. Now, having joined the ranks of the worried, her belated conversion to the idea could seal her doom.