There has been speculation there could be a hung Parliament next year
The Liberal Democrats have rejected a claim by David Cameron that there are now fewer policy differences between the two parties than in the past.
In his new year message, the Tory leader said there was "a lot less disagreement than there used to be" on how to create a fairer Britain.
But Lib Dem chief of staff Danny Alexander called the comments "vacuous spin" that were "fooling nobody".
He said Mr Cameron appeared "confused" about the meaning of fairness.
The Conservatives have been making friendly overtures to the Liberal Democrats in recent months, with some opinion polls suggesting a hung Parliament the most likely outcome of next year's general election.
In that situation, Lib Dem leader Nick Clegg would be faced with a choice between forming a coalition with Labour or the Conservatives in order to provide either Gordon Brown or David Cameron with a working Parliamentary majority.
Conservative Party chairman Eric Pickles stepped up what has been called his "love bombing" of Lib Dem voters in an interview with BBC Radio 4's PM programme.
"What I am seeking to do is to say to a number of constituencies currently held by Liberal Democrat MPs, the only real way of achieving those ideals of liberal democracy is by voting Conservative," he said.
He said climate change - an issue on which he claimed David Cameron had led the other parties - was a "practical example" of why Lib Dem supporters should vote Conservative.
"We can go on with the old system as before and vote tribally or we can embrace what David Cameron is saying and let's govern, let's work together, on the basis of consensus," he added.
But his overtures were firmly rejected by Danny Alexander, who described them as "meaningless mush".
He told PM: "Everybody knows that on issues like fairness and on the environment the Conservatives cannot be trusted."
He added: "I want to see change. Reshuffling the deck chairs on the Titanic is not going to change direction. What you need is a government that would genuinely do things differently - that would make the country fairer, that would really value the environment.
"And I believe the only way to get that is by voting Liberal Democrat."
'Good clean fight'
Mr Clegg has said he will support the party with the biggest mandate in the event of a hung Parliament, without specifying whether that would be the party with the most votes or the most seats.
Lib Dem members are thought likely to resist any alliance with the Conservative party, but Mr Clegg may find it difficult to sustain a Labour government in power if they are not the largest party, as the polls suggest may be the case.
In his Christmas message, Mr Cameron said he hoped for an election "free from fake political dividing lines".
"I don't think we should invent differences where there aren't differences," he said.
"Let's be honest that whether you're Labour, Conservative or Liberal Democrat, you're motivated by pretty much the same progressive aims: a country that is safer, fairer, greener and where opportunity is more equal.
"It's how to achieve these aims that we disagree about - and indeed between the Conservatives and the Liberal Democrats there is a lot less disagreement than there used to be."
He added that "a hung Parliament would be bad for Britain" despite this apparent political overlap.
Mr Cameron also used his message to call for the general election campaign to be a "good clean fight".
His appeal follows speculation that Labour may be planning to fight a "class war" with the Tories, making Mr Cameron's own privileged background a political issue.