ALTHOUGH the government's honeymoon with voters ended long ago, the love-in between the partners in coalition lasted almost a year. Differences between Conservatives and Liberal Democrats were aired privately. Relations between senior figures were effortlessly cordial. As recently as last month, Nick Clegg, the Lib Dem deputy prime minister, was caught joking with David Cameron, the Tory prime minister, that the pair would never find anything to disagree on. It was even suggested that coalition could lead to an electoral pact or outright merger.

Suddenly, the bonhomie has gone. A vicious campaign before the referendum on May 5th on whether Britain should adopt the alternative-vote (AV) electoral system (see article) has seen to that. The Lib Dems, who support the change, accuse the Conservatives, who do not, of exploiting the unpopularity of Mr Clegg. Chris Huhne, the Lib Dem energy secretary, has threatened legal action against Tory colleagues over their claims about the cost of converting to AV. Vince Cable, the left-leaning Lib Dem business secretary, has provoked Tories by suggesting gleefully that AV could lock them out of power in future. It may sometimes suit both partners to play up their disagreements but the current enmity is thought to be genuine.

Whatever the result of the referendum, the coalition will be wounded. A rejection of AV (which polls suggest is likely) could push Lib Dems who prize electoral reform above all else into seeking a way out of coalition. A challenge to Mr Clegg's leadership, perhaps from Mr Huhne, is mooted. Mr Cameron will have to give the Lib Dems some sops, such as progress towards an elected House of Lords, to ease the hurt.

But a vote in favour of AV could cause more damage in the long run. Tory MPs, who believe that Mr Cameron agreed to the referendum too easily after fluffing a general election that he should have won outright last year, will resent their leader deeply. They will demand compensation in the form of right-wing policies, which would gradually push the parties further apart. Things are so bleak that there is even talk of a snap election this year.

In reality, that is unlikely to happen. Indeed, the smart money is still, just about, on the coalition to last the scheduled five years. The Lib Dems, who are doing badly in the polls, have no incentive to provoke an early election. The Tories' support is holding up; they regard Labour's poll lead as soft. But they are not confident of winning a working majority in Parliament this year. Moreover, the coalition was never built on good personal relations alone. In their negotiations last May, the two parties found themselves agreeing on many issues, including fiscal policy and public-service reform. That has not changed.

Far more likely than a break-up is a tetchier relationship, with the Lib Dems stressing their differences with the Tories. But acting like an opposition within government could win short-term popularity among voters at the cost of long-term respect. Mr Clegg's strategy thus far has been to ensure that his party “owns” everything the coalition does. Only then, he calculated, would it get credit if the government is eventually seen to be a success.

The referendum is not the only thing on the ballot on May 5th. Adding to the sour mood in government are the losses both parties expect to suffer in elections being held on the same day in 279 English local authorities and to choose the devolved legislatures of Scotland, Wales and Northern Ireland. The campaign has been almost as bitter as the tussle over electoral reform. Conservatives have accused Labour-run councils of responding to reduced grants by making cuts to vital services rather than waste and bureaucracy, all for the sake of turning voters against the coalition. The Tories fear that they might lose the bulk of the 900 council seats they gained in the equivalent round of elections in 2007.

As for the Lib Dems, if they lose ground to Labour in the north of England—ceding control of places such as Newcastle and Stockport—the country will look increasingly divided between a prosperous, pro-coalition south and a resentful north. In 2007 the party scored 26% of the vote. They are currently polling at around 10%.

It is of some small comfort to the coalition that many of the most vulnerable Tory councils in England can realistically be gained only by the Lib Dems, and vice versa. But May 5th will still be a good day for Labour. A strong base of councillors gives parties the infrastructure and local prominence to campaign effectively in general elections. Labour has already begun to rebuild the support that withered while it was in power—it did surprisingly well in last year's local elections—and is likely to make further gains. Labour may also prevail in Wales, though the Scottish Nationalists are ahead north of the border.

The aftermath of May 5th will be the biggest test so far of the coalition's togetherness, and perhaps of Mr Clegg's grip on his party. Even if it is passed, next year will be just as hard, as spending cuts bite. Optimists in government urge doubters to train their eyes on this parliament's later stages. The economy should be growing smoothly by then, and the structural fiscal deficit largely erased. Time should have healed the wounds opened by AV. They are probably right that 2014-15 will look better for the coalition than 2011-12. Staying together until then is the challenge.