* Cameron could come under pressure from right wing
* Party pledges to stick to its campaign strategy
* Polls show lead over Labour eroding
By Adrian Croft
LONDON, Feb 28 (Reuters) - Britain's opposition Conservatives may tone down their tough message on the need to rein in the gaping budget deficit after a poll showed they could lose an election due by June.
The slump in the Conservatives' ratings, after months in which they looked certain to return to power, could also lead party right-wingers to press leader David Cameron to change his centrist campaign strategy, although he is likely to resist.
"The Conservatives should be concerned about it because, given the unpopularity of (Prime Minister) Gordon Brown, the Conservatives should be comfortably ahead. That suggests something is going wrong for them," said Neil Carter, politics professor at York University.
The Conservative lead over Labour, in the double digits until recently, fell to just two points in a Sunday Times/YouGov poll, reviving Labour's hopes of extending their 13-year rule in an election that Brown must call by June 3. [nUKPOLLS10]
Under Britain's first-past-the-post, constituency system, that result would give neither party a majority in parliament but Labour would have more seats and be in pole position to form the next government, either as a minority or in a coalition.
The poll came as a shock to the Conservative Party faithful, gathered for their last conference before the election in the south coast resort of Brighton, but party leaders said it was just one poll and they remained confident of winning.
"We are in good shape at the moment. If the election was held today we would win it with a majority in parliament," the party's foreign affars spokesman William Hague told Reuters in an interview.
HUNG PARLIAMENT?
Other recent polls have also pointed to a "hung parliament", albeit with a Conservative win short of an absolute majority.
"It's a concern to all of us and I find it extraordinary that people still don't see the culpability of successive Labour governments in the mess we are in," said Georgina Butler, who is seeking to become a Conservative candidate in the election.
The prospect of a hung parliament frightens financial markets, which fear a minority or coalition government would shy away from tough action on the deficit, set to exceed 12 percent of GDP this year, a level similar to that of crisis-hit Greece.
Labour plans to halve the deficit in four years with cuts starting next year, but says turning off economic stimulus taps now could derail a tentative recovery from a deep recession.
The Conservatives say this is too little, too late. They pledge to make an "early start" on deficit cutting if they win power, saying delay could cause a crisis of investor confidence and push up interest rates, but have not given any figures.
The Conservatives' uncompromising message on the need for belt-tightening may have turned off some voters, who fear public spending cuts could lead to job losses and poorer services.
"The 'age of austerity' is a sound bite too far," said Tim Bale, senior lecturer in politics at Sussex University and author of a recent book on the Conservatives.
The Conservatives had been trying to tone down the austerity message, "but that gets them into accusations of double-talk", he said.
The polls may reflect a series of recent blunders by the Conservatives, while Labour may be getting some reward for the economy emerging from recession towards the end of 2009.
The tighter polls could bring increased pressure on Cameron from the right wing of his party to go back to emphasising traditional Conservative themes such as immigration, tax-cutting and opposition to closer European integration.
PRESSURE FROM THE RIGHT
The youthful Cameron, who gave a polished speech to the conference without notes, has dragged the Conservatives towards the political centre since becoming leader in late 2005, hoping to make the party once dubbed the "nasty" party electable again.
His policy of protecting the state-run National Health Service and helping the poor has not gone down well with traditionalists wedded to free-market, shrink-the-state views.
"You've begun to see signs of 'Can't we bring immigration back again? Isn't it time to talk more about corporation tax cuts?' You will almost certainly see pressure on Cameron, but he maintains he is not going to give in to that kind of pressure," Bale said.
A senior party official said the Conservatives would not start changing their message because of the tightening polls.
The party would keep pushing the message that the election is a choice between five more years of Labour and change under the Conservatives, he said.
The Conservatives will cut company taxes for big firms to 25 percent from 28 percent if elected, a party source said on Saturday. [ID:nLDE61Q06M]
"Being seen to be the toughest on tackling the deficit hasn't helped recently, so I suspect this latest message (company tax cuts) is designed to help the Tories' (Conservatives') softer side. I think they are trying to balance the message," said Alan Clarke, UK economist at BNP Paribas.