In the fragrant rose garden behind No. 10 Downing Street, David Cameron and Nick Clegg presented themselves to the British public one year ago as a political dream team: Cameron, a Conservative, as prime minister and Clegg, a Liberal Democrat, as his deputy, in a coalition government blurring the lines between the right and left wings.

Yet as Britons vote in a referendum Thursday that could change the way they elect their governments, the coalition is no longer smelling so sweet.

Cameron’s Conservatives grudgingly agreed to the referendum to appease the Liberal Democrats — traditionally Britain’s third-largest political force after the Conservative and Labor parties and whose support Cameron needed to form a government after a close vote last May. But passage of the ballot measure would arguably aid the Liberal Democrats the most, while hurting the Conservatives in future elections. The Conservatives are being accused of waging a misinformation and smear campaign against their own coalition partners, the Liberal Democrats, to defeat it.

After talking up the fraternal bonds of political friendship only months ago, Clegg is now lashing out at the Conservatives for spreading “lies” and “deceit.” The tension spilled over into a cabinet meeting Tuesday, when the Liberal Democrats’ energy secretary confronted Cameron over campaign materials opposing the measure that contained personal attacks against Clegg.

The open warfare over the referendum is damaging the coalition, potentially testing its ability to hold together as planned for a full five years. The Liberal Democrats are vowing that win or lose, they will more aggressively challenge Cameron’s Conservative agenda after Thursday’s vote. Already, the Liberal Democrats in recent weeks have come out swinging against Cameron on issues including immigration and heath-care reform.

Britain's Prime Minister David Cameron (R) and Deputy Prime Minister Nick Clegg are pictured through railings at they arrive for a Q&A on health issues with NHS staff during a visit to Frimley Park hospital, southeast England. (LEFTERIS PITARAKIS/AFP/GETTY IMAGES)

“The first 12 months, there was a bit of an embed [with the conservatives], but now it is time for us to flex our muscles a bit,” Tim Farron, the Liberal Democrats’ party president, said in an interview.

In the balance, however, is not only the durability of the coalition government but also a major shift in the voting system.

The ballot measure would dump the current system that elects members of Parliament by simply awarding victory to the candidate with the most votes. It would be replaced with a system similar to the one now used to pick the best picture at the Academy Awards, with voters ranking the candidates in order of preference and the losing candidates’ votes then redistributed.

The Liberal Democrats see it as a major steppingstone toward more radical electoral reform. But in theory, even the change on Thursday’s ballot could give the Liberal Democrats more of a fighting chance against the Conservatives and the Labor Party in a few dozen electoral districts.

But for those supporting the change — including the Liberal Democrats and some in the Labor Party — Thursday’s vote will be an uphill battle. Polls showed strong public support only a year ago, but more recently they have pointed to far less enthusiasm, with a majority now favoring the current system. Some analysts attribute the erosion to the fact that electoral reform has become inexorably tied to the image of the Liberal Democrats. They have suffered a dramatic loss of support after the decision to enter into a coalition with the Conservatives, a party anathema to many in the Liberal Democrat grass roots. The image of Clegg — once seen as a political dynamo — has suffered the most. He even begged voters this week not to reject the measure simply out of a desire to “poke me in the eye.”

A defeat of the measure would mark a severe blow to the Liberal Democrats, whose decision to enter into a coalition in the first place was based in part on the promise of holding a vote on election reform. That defeat could be made profoundly worse by the results of various local elections also being held Thursday, with the Liberal Democrats set to sustain heavy losses, particularly in England and Scotland.

Yet for now, the Liberal Democrats are insisting that they will stay the course of the coalition, arguing that it remains essential to cutting the national debt and getting Britain’s financial house back in order.

“The fact is, neither the Conservatives nor the Liberal Democrats would gain from dissolving the coalition early, as it would only prompt new elections,” said Iain McLean, a professor of politics at Oxford University. “And when the country is going through huge budget cuts, this is not a time when either party would want to face the electorate.”