Transport Secretary Justine Greening has admitted it would be "difficult" for her to stay in Government if it backed plans to expand Heathrow.
Ms Greening, a prominent campaigner against a third runway which would affect her London constituency, insists there is still a consensus against the development.
But senior Conservatives are becoming increasingly vocal about the need for expansion in order to increase capacity and shore up Britain's ailing economy.
In the latest intervention, Tim Yeo has called on Prime Minister David Cameron to decide whether he is a "man or a mouse" and drop his objection to the plans.
The former environment minister, who also chairs the Commons energy committee, used to oppose expansion but now says the environmental objections are disappearing.
Mr Yeo, writing in The Daily Telegraph, suggested backing the expansion would give the Government a "sense of mission".
"The Prime Minister must ask himself whether he is man or mouse," he said. "Does he want to be another Harold Macmillan, presiding over a dignified slide towards insignificance?
"Or is there somewhere inside his heart - an organ that still remains impenetrable to most Britons - a trace of (former PM Margaret) Thatcher, determined to reverse the direction of our ship?
"An immediate go-ahead for a third runway will symbolise the start of a new era, the moment the Cameron government found its sense of mission. Let's go for it."
Later, the MP claimed the tide was turning over Heathrow and urged the Prime Minister to show "political courage", although he denied he was "throwing down a gauntlet".
He insisted he was still one of Mr Cameron's "well-wishers" in the Tory party but stressed he should be prepared to change tack to reflect the current climate.
Mr Yeo called on the PM to show a "bit of steel on the economy" and suggested he should face down the Lib Dems if they oppose him.
But Ms Greening said "it would be difficult for me" to stay in Government if policy on a third runway shifted.
The Transport Secretary insisted expansion at Heathrow would be the wrong move because it would become rapidly outdated and said a wholesale review of air capacity is needed instead.
"I don't think any of the facts have changed around a third runway," she told the BBC.
It has been mooted that Ms Greening could leave her post in the upcoming reshuffle to remove any problem over a change in airport policy but she says she wants to stay on.
"It's a fantastic job, I think we've done an awful lot in the 10 months I've been in the role," she said.
Challenged on whether Mr Cameron was a man or mouse, London Mayor Boris Johnson said: "I think he's a man of dynamism and greatness and he will seize the moment to give this country the long term solution that it needs."
"It is plain the argument over aviation capacity is not going to vanish, You can't long grass this, it is necessary to come up with an answer. Business needs an answer and I've no doubt the Prime Minister is going to provide one."
Deputy Prime Minister Nick Clegg said Heathrow expansion could not happen because it was against the coalition agreement.
But he insisted this did not mean ministers would "stick our heads in the sand" and vowed to look at capacity and how to maintain the UK's international links.
"There are lots of ways of doing that and we shouldn't just lurch to one solution because one individual MP was to say so," Mr Clegg said.
A Downing Street spokesman added: "The coalition parties have made a pledge not to have a third runway and that is a pledge that we will keep. We don't see the argument for a third runway."
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