The Tories have no chance of winning next month's key Oldham East and Saddleworth by-election, Liberal Democrat Business Secretary Vince Cable declared today.
But he denied suggestions the Conservative Party was holding back in the contest to give its coalition partner a better chance of victory.
Prime Minister David Cameron fuelled suspicions of a deal last week when he wished Elwyn Watkins, the Lib Dem candidate in the January 13 poll, well and said he hoped for a "friendly" campaign.
Mr Watkins missed out on the seat by just 103 votes in May, but the result was declared void last month by an election court which found that victorious Labour candidate Phil Woolas had made false statements about him.
Although Mr Watkins is Labour's nearest challenger, the constituency was a three-way marginal in May, with Conservative Kashif Ali - who is standing again - less than 2,500 votes behind.
But asked about the Prime Minister's intervention, Mr Cable told BBC1's Andrew Marr Show it was a "straight fight" between his party and Labour.
"We have not got his support. He is putting up his own candidate and people can compete.
"But I think people in Oldham can do the arithmetic and can see that this is a straight fight between the Liberal Democrats and Labour and they can make their calculations on that basis."
Labour has selected Debbie Abrahams as its candidate.
The by-election is being seen as an indicator of how the two parties in the coalition Government will behave when pitched against one another in the fight for votes.
Mr Cameron has confirmed he will visit the constituency to campaign for Mr Ali, who he described as "a very strong candidate", and insisted Tories would be "fighting for all the votes".
But he took the unusual step of saying he wished the Lib Dems well in the by-election because of Mr Watkins' experiences during the general election campaign.
Mr Cable also expressed confidence that the Lib Dems were strong enough not to be torn apart by the tuition fees controversy - which saw its MPs split three ways in the Commons.
"We have had the most difficult test we could possibly have had over this tuition fee issue. We knew it was politically going to be difficult.
"I am confident that having dealt with it, and having dealt with the difficult politics, we've actually got a good policy," he said.
And he rejected claims he had fallen out with party leader Nick Clegg over his decision to appear on the Christmas special edition of Strictly Come Dancing.
"He has been very supportive, as have my colleagues," he said.
"I work very hard - sometimes an 80-hour week - I need something to keep me fit and sane. Dancing is my hobby so why not do it in this way?"
Former Liberal Democrat leader Charles Kennedy indicated that he believed the result of the by-election could be much closer - and give the first clear indication of public opinion of the coalition.
He told Sky News: "I think the idea of the coalition is popular in itself with mainstream opinion. A lot of the policies aren't popular, that is probably going to accelerate over the course of next year, no doubt about that, as the cuts begin to bite.
"That was inevitable whoever was going to be in power.
"But the impact on the individual parties is extremely unpredictable, which is why in another two or three weeks we will all be discussing the result of the Oldham by-election.
"God knows what is going to happen there, but that will be a very interesting first tangible guide in a three-way, four-way marginal seat...as to what people actually think."