Political strategists are obsessed with messages that "cut through". They mean the bits that somehow penetrate the consciousness of those people who don’t spend all their time thinking about politics, which is pretty much everyone.

Inconveniently, politicians are often surrounded by other politicians and journalists. They (we) are often as bad as each other at remembering an axiomatic truth about whatever it is they (we) have just said or written: most of the time, no-one cares.

So I do not mean to belittle the Liberal Democrats at their annual conference when I say that most of what passes as "news" – and what animates the chatter in the hotel bars of an evening – will skim off the surface of voters’ minds without leaving a mark.

I’d guess that two things have "cut through" in politics in the last week. First, that Nick Clegg is sorry. It might not be entirely clear what he is sorry for. We know he regrets making a pledge not to raise university tuition fees when he wasn’t remotely sure he could keep it. We know also that he stands by the policy on tuition fees currently in place. He is frustrated because the episode haunts his party, casting him as the emblematic face of broken promises and making it impossible to get any other messages heard. So, after much deliberation, Clegg decided to lob a contrition grenade – hardly a precise weapon, but sufficient, he hopes, to enable him to change the subject.

The Deputy Prime Minister’s aides insist his video apology is not meant to solve an image problem overnight (and plainly it hasn’t). The test of its effectiveness, they say, will only come towards the end of the parliament, when campaigning for a general election starts up. The hope is that, by then, it will seem tired and petty for Clegg’s rivals to attack him as the king of paltry pledges. He’s said he’s sorry – not a lot of politicians do that – what more do you want? It’s a pretty optimistic line, but probably fractionally better than the alternative, which was not apologising.

There are voters who will never forgive Clegg, whatever he says or does. They are lost to the party for the foreseeable future. As for the rest, given that one of the few things everyone knew about the Lib Dem leader is that he broke a promise, it is probably a small net positive that one of the other few things people now know is that he is also sorry. The details don’t matter so much. That’s cut through.

The second thing that has probably registered on most people’s political radars is that a senior Conservative member of the cabinet might or might not have called a police officer "a fucking pleb". Quite how toxic that is for the Cameron project hardly needs spelling out – it underlines the image of the Prime Minister as surrounded by a haughty, wealthy clique that is out of touch with the lives of ordinary people. Worse, it gives the impression that they despise public servants. Whether or not Andrew Mitchell actually said the words attributed to him – and he denies it – is hardly relevant. What counts is that it resonates as the sort of thing a millionaire, ex-banker Tory might be expected to say. Unfair, maybe. But that’s how cut through works.

The strong impression I get from speaking to senior Lib Dems here in Brighton is that they think Cameron ought to have jumped on the whole episode harder and faster. He should, they suggest, have seized it as an opportunity to trumpet his abhorrence at the attitudes attributed to his chief whip, declaring that there is no place for such language in a modern Conservative party. It is probably too late now. Whether Mitchell survives or not, the damage is done.

The Lib Dems aren’t too upset about that. It suits them to be seen as the reasonable, down-to-earth, humble face of the coalition as distinct from the moneyed arrogance of their partners. Predictably, Vince Cable exploited the opportunity to salt the Tory wound in precisely that way by proudly declaring himself to be a "pleb" in his conference speech. One senior Lib Dem, wearing a broad grin, yesterday described the whole Mitchell episode to me as  "dynamite!" A conference stall selling Lib Dem memorabilia sold out of badges announcing "I’m sorry" in the first days of the conference; "pleb" badges quickly replaced them as the must-have accessory.

But the relish with which Lib Dems are enjoying watching the Conservatives re-contaminate their brand does not sit entirely comfortably with the hope that Clegg’s apology will win the party a new audience.

In theory, it should be possible for the two episodes to cut through simultaneously in a way that helps the junior coalition partner. "Behold," the Lib Dems cry, "what we have to put up with! Yes, we made some mistakes, but aren't you glad we're here to rein these beastly Tories in. Imagine what they’d be like without us. The horror! We may not have won every battle - we handled that tuition fees thing all wrong - and yet we are winning some battles too." Then they hope their message of fairer taxes - making the wealthy carry more of the burden of austerity - will be heard and earn them some political credit.

But Tory toxicity is not specific to any policy. It is also contagious. It is a cultural apparatus that surrounds great tranches of the population, especially in the north and Scotland, as well as many younger voters and minority communities (as some glum Tories regretfully concede in private). It is a kind of political inoculation against putting a cross in a certain box come polling day. It is the force that stopped David Cameron from winning a majority. In that sense it is obvious that the Lib Dems should want to nurture the most vicious caricature of their governing allies – and hazardous.

There is ample evidence that the junior coalition party struggles to assert its identity in partnership with a much mightier political beast. Attempts at "differentiation" to overcome that problem have focused largely on policy. But individual policy rarely cuts through – especially when the question of credit and blame for good government in this parliament is largely dependent on the performance of the economy.

There is always the prospect that the Lib Dems are seen to be gathering up only crumbs of policy compensation in exchange for complicity in a largely Conservative project. And in that case, reveling in Tory toxicity is not risk-free.

While there is some disappointment in Brighton that Mitchell’s story has blown the conference out of the headlines, there are still a large number of people of in the party who see the  "pleb" episode as anything other than an open goal – and they’ll keep banging the ball in. It is hard to begrudge them that opportunity at their annual conference, since the occasion is all about celebrating the party’s distinctiveness and independence. But then the business of government must resume and the Tories will not have ignored the pleasure that was taken in their discomfort nor will they forget it. The task of managing coalition effectively, demonstrating that it can be a functional system of government, is as important a prize for the third party as differentiation from the Tories.

The lesson of the past two years is that, when the Conservative party feels wounded and insulted by the Lib Dems, it retaliates by demanding that Cameron ignore Clegg and crush his policy ambitions. The Prime Minister always acquiesces.

So the risk is that gleeful – and from the Tory point of view, gratuitous – punching of a bruised brand accelerates a process that ends up with the Lib Dems getting less out of coalition and looking more like helpless passengers. It is one thing for voters to know that Nick Clegg feels bad about handling one policy wrong. But if the two things they know are that he is sorry and that he doesn’t get his way, what cuts through is the sense that the Lib Dems are apologising for the basic fact of having propped up a Conservative government but not sorry enough to do anything about it.