The rebuff came as the issue of spending cuts continued to cause ructions, with claims that the parties were now in a “race to the bottom”.

The Tory leader said that in areas like civil liberties, education and climate change, there was “barely a cigarette paper” between the two parties.

He added: “If you want rid of Gordon Brown and the big brother state, and if you care about our schools, our quality of life and our liberties, then join us in one national movement that can bring real change.”

However, Mr Clegg rejected Mr Cameron’s approach, insisting the two parties were “totally different”, citing issues like taxes and Europe.

Yet the Lib Dem leader refused to discuss whether he would enter coalition talks with either Labour or the Tories in the event of a hung parliament after the General Election.

Meantime, Charles Kennedy, the former party leader, appeared to rule out one option after making clear Lib Dems could not enter a coalition with the Conservatives because of their hostility towards Europe.

“It’s always seemed to me that this is one of several straws that would break any camel’s back. I just don’t see how we could make common ground with a Cameron-Hague administration on the European issue. I mean pigs would fly,” he told a fringe meeting.

Elsewhere, Ed Balls, the Schools Secretary, suffered a backlash after suggesting a £2bn cost-cutting programme in English schools.

He proposed axing up to 3000 deputy heads and other senior posts in merging some schools’ administrations to find cash to fund frontline services.

However, he was warned by furious unions the “disastrous” merger plan would impact on the classroom.

In a separate development, Labour launched a furious attack against Tory claims the UK Government planned a secret income tax rise.

George Osborne claimed leaked Treasury figures showed a £14.8bn rise in expected revenues in 2011/12 – the equivalent of a 3p rise in the income tax rate – which could not be explained by a predicted economic recovery.

However, ministers pointed out the figures were published in the April Budget, denied any hidden tax-raising plan and accused the Tories of “the politics of the big lie”.

Liam Byrne, the Chief Secretary to the Treasury, accused the Shadow Chancellor of misleading voters and engaging in “schoolboy” politics.