A good slogan should be pithy, memorable and pack as much meaning as possible into a few short words. But the Liberal Democrats’ new tagline – “Demand Better” – feels as though it says a little too much.

You can see the thinking behind it. The catchphrase speaks to the Lib Dems’ major opportunity, when the United Kingdom’s big two political parties are both widely disliked. “Don’t know” regularly tops the charts when voters are asked to pick which of Theresa May or Jeremy Corbyn would make the best prime minister. More than one in ten Tory voters dislike May, while a third of Labour voters don’t want Corbyn to replace her.

In addition, the brand of politics that the Liberal Democrats are selling – pro-European, socially liberal – is well-liked by the commentariat, which ought to guarantee a sympathetic hearing for what used to be Britain’s third party.

However, as one senior Liberal Democrat recently told me, the problem with “Demand Better” is that the slogan “is a great attack line – against our enemies, and ourselves”. Another complains: “I can’t help reading it in a sarcastic voice.”

One of the less glamorous jobs of a political adviser is staying alert for photo opportunities that could make an embattled leader’s position worse: an ITV reporter heard that Downing Street went so far as to ban Dalmatians from a photoshoot at a dog sanctuary, in order to avoid comparisons between May and Cruella de Vil.

I recently went for a drink with a former staffer who has traded politics for the private sector. He told me, entirely seriously, that he had yet to train himself out of scoping out whether a room had any Exit signs in them, to avoid the unfortunate visual metaphor of his flailing boss next to a departure logo. Having “Demand Better” splashed all over the stage at the Lib Dems’ autumn conference in Brighton, including the podium where Cable and others will speak, is a needless own goal.

The image of Cable next to the slogan will be particularly painful to party staffers. The Lib Dem leader has only been in post for a year, but had to fend off succession questions again last week after Business Insider reported that an upcoming speech on 7 September would discuss, among other things, his own future plans.

Speculation about Cable’s future has three foundations. The first is simple ageism. If this parliament runs its full length, Cable will be almost 79 at the time of the next election in May 2022. Even his most vicious internal critics concede that what they see as his mistakes cannot be pinned on his age, per se.

Yet there are endless grumbles about what his age means: he has been at the top of Liberal Democrat politics for close to three decades, and an enthusiastic combatant in many of the party’s internecine conflicts. He is seen as having conspired to bring down both Nick Clegg (unsuccessfully) and Ming Campbell (successfully). The criticism of Campbell, then just 65, was that he was “too old”, which adds a note of either irony – or, if you ask some of Campbell’s old allies, karma.

During the coalition years, there was a feeling within Team Clegg that while Tim Farron might have been transparently plotting his path to the leadership, at least he was content to win it in his own time. Cable was seen as actively manoeuvring to bring the Clegg era to an early end.

Added to ageism and past grievances is a feeling that the party should be doing better in the polls. Voters have a choice between a Conservative leadership that is too weak to censure an Islamophobe and a Labour leadership mired in accusations of anti-Semitism, with both parties committed to a form of Brexit that is unacceptable to a significant percentage of the country. Yet the Liberal Democrats are still bobbing along at just shy of 10 per cent in the polls. The only time the party commands any attention is when the topic of Cable’s future is in the news. Surely they could and should be doing better?

In the real world, though, Cable’s Liberal Democrats aren’t doing badly – quite the reverse. They gained more council seats than any other political party in the local elections in May. They retained control of the Watford mayoralty, a particularly impressive feat considering the retirement of their popular incumbent, Dorothy Thornhill. It might receive little attention in the press, but Cable’s mission to turn the party into an “ideas factory” (as it was under Paddy Ashdown) has seen it announce a series of substantial policies, from a new hypothecated tax to abolishing Ofsted. Even the party’s poor polling is an improvement on its resting average under Farron.

The difficult truth for the Liberal Democrats is that the party’s biggest problems are structural. A little more than half the electorate regards the Lib Dem participation in coalition as a sin that has not yet been forgiven. Of the remaining 50 per cent, only half support the party’s call for an EU referendum rerun. Any new leader would still need to account for the party’s time in government, and while an anti-Brexit position may yet reap electoral dividends, it hasn’t yet.

It’s true that many voters dislike both May and Corbyn. Yet it’s also true that very few voters dislike May and Corbyn equally. Thanks to first-past-the-post, if your number one priority is to defeat May, you will likely vote Labour; and if your main political objective is to stop Corbyn entering Downing Street, you will vote Conservative. And that’s the real problem with “demanding better”: voters know full well that the cost of opting for an upgrade on a party they dislike might be victory for a party they loathe.