Few sentiments pollute political judgement like the feeling of having been betrayed. Most Tory MPs worry about losing the next election but the level-headed ones recognise that David Cameron remains the strongest available candidate to lead them into that battle. For the minority that want an immediate change of leader, electoral calculation is subordinate to rage against the Prime Minister for conspiring to snuff out the flame of true Conservatism. Most voters have no idea what that means, just as they have no attachment to a venerable “Labour tradition” that Ed Miliband is always liable to be accused of traducing.

It is Liberal Democrat MPs who seem the least driven by puritanical notions of what their party is supposed to represent. Labour and Tories say that proves an innate lack of principle. Lib Dems prefer to see it as pragmatism, born of the obligation on a small party to compromise if it wants to see its policies enacted.

That could be an attractive trait. The public warms to a non-partisan spirit, as the coalition’s rose-scented honeymoon showed. Compromise looks less appealing when cast as stitch-up or sell-out, which is what political tribalists smell in cross-party collaboration. Nick Clegg’s misfortune is to have partnered with a party that is hostile to the idea that coalition should form part of the standard repertoire of British politics. Tories see it as a distasteful one-off episode; a toilet break at the policy service station on the road to Conservative hegemony.

Mutant cousin

The same problem would arise in an alliance with Labour. There is a strong feeling in the opposition ranks that Clegg’s outfit, carrying both liberal and social-democrat DNA, is a mutant cousin of the real left. By installing Cameron in Downing Street, the Lib Dems completed, in Labour eyes, an arc of historical treachery.

The Labour leadership, calculating the probability that the next parliament will again be hung, takes a more nuanced view. In recent months, fragments of complicity with Vince Cable, Lib Dem Business Secretary, have surfaced: some text-message exchanges with Ed Miliband; a hint of tax policy proximity from Ed Balls. These overtures are tolerated by the Labour faithful only on the assumption that the motive is mischievous – to undermine Clegg and destabilise the coalition. (That is the interpretation in the Deputy Prime Minister’s office. Clegg loyalists deride Cable’s micro-flirtation with Labour and dismiss chatter about his leadership ambitions as naivety amplified by vanity.)

Labour has to hate the coalition for locking it out of power but the arrangement has not been wholly disastrous for a party crawling unsteadily back from electoral mauling. It awarded Miliband a monopoly on opposition in Westminster. At first, shadow cabinet ministers belittled that boon, complaining that a media obsession with the novelty of coalition deprived them of an audience. Given how slow Miliband’s policy formation has been, a lack of public scrutiny was not such a hindrance. No one was listening to Labour at the point when they had nothing much to say.

Then, as coalition relations soured and the intimacy of the early months threatened to dissolve Lib Dem identity, the party embarked on a strategy of “differentiation” that abetted Labour’s attacks on Cameron. Clegg’s implicit message has been that Conservative instincts are as sour as they were when the “nasty party” label hung around their necks. Coalition is meant to sweeten the mix.

Labour dismisses the Lib Dems’ policy contribution to government but they cannot deny that the junior partner’s assertiveness has provoked the Tory right and undermined Cameron’s authority. It has forced the Prime Minister to neglect the already atrophied liberal wing of his own party, meaning the project to modernise and “decontaminate” the Tory brand has stalled.

Senior Lib Dems cite backbench Conservative fury as a measure of their impact on policy and so a refutation of Labour’s assertion that Clegg’s role is negligible. The Deputy Prime Minister is presented as the voice of moderation at the centre of a hysterical, partisan fray. “When left and right are both screaming with the volume turned up to 11, with contradictory stories, it would suggest that we are doing something right,” says one senior Clegg aide.

Downing Street depicts Lib Dem identity-hunting as nostalgia for the kinds of soft left positions that many voters hate: pro-Europeanism; squeamishness about welfare cuts; tolerance of immigration. “The things they can differentiate on are issues where the public are somewhere else,” says one senior Tory source.

Unarmed sentry

Mindful of that hazard, the Lib Dems are making “fairer tax in tough times” the theme of their annual conference. They hope to remind the country that they own the only popular policy from an otherwise disastrous Budget – raising the income-tax threshold for low earners – and plan more in the same vein. The Tories are then left holding toxic tax cuts for the rich.

Labour will continue to heap personal scorn on Clegg as an unarmed Cameron sentry. Even loyal Lib Dems accept that their leader’s image as a serial breaker of promises is proving hard to shift. But the challenge of restoring confidence in Clegg, they insist, is inseparable from the task of showcasing coalition as an attractive model of government. The hope is that, over time, some of the choices currently seen as betrayals can be presented as compromises made necessary by the pursuit of nobler ends. Regicidal rumblings are cast as a temporary wavering of nerve.

It is a long shot. But there is sure to be a slice of the electorate that will have more sympathy for the dilemmas the Lib Dems have faced than is felt in the tribal Labour and Tory camps; enough, perhaps, to save the third party from destruction at the next election. If that poll does indeed produce another hung parliament and Ed Miliband is in a position to form a government, it will be in no small measure because Clegg has hemmed the Tories into an ideological corner from where, history suggests, they struggle to reach a majority. That isn’t the reason most Conservative MPs, obsessed with the contamination of their purest policy ambitions, are angry with the Lib Dems. It is a reason why they should be.