The most important and urgent task facing the new Labour leader to be elected this afternoon will be to decide the party's line on public spending.

Officially, Labour is committed to halving the public deficit over four years with £44bn of cuts, a slower and less severe stance on cuts policy than the Chancellor, George Osborne, who wants to eliminate the structural deficit over five years with £83bn of cuts.

But Labour's policy may have a limited shelf life. Alistair Darling, the Shadow Chancellor, has stuck to the one he implemented at the Treasury. Among the leadership candidates, the Darling stance has been endorsed by David Miliband and Andy Burnham but not by Ed Miliband, Diane Abbott or Ed Balls, who has argued powerfully that the Coalition Government may be making a catastrophic mistake by cutting so quickly. Even opponents believe he has earned the right to be Shadow Chancellor.

Yesterday Harriet Harman, the acting leader, became the latest Labour figure to question the official line.

Even when Labour was still in power, its position on the deficit was hardly rock solid. Gordon Brown was cajoled by Mr Darling and Peter Mandelson into using what Labour insiders called the "C-word" – cuts – but it's clear from the post-election books and interviews that the then-Prime Minister didn't really believe in it. He was never fully weaned off his favourite theme – Labour investment versus Tory cuts. Mr Brown believed Mr Darling was taken prisoner by cautious Treasury officials and didn't stand up to them in the way that he had done as Chancellor. In private, he often railed against Treasury orthodoxy and wanted to install Mr Balls, but Mr Darling saw that off by warning he would go to the backbenches rather than the Foreign Office. Mr Brown lacked the strength to oust him. One irony of his largely unhappy three years as Prime Minister is that he enjoyed more raw power as Chancellor. Like Mr Balls, he wanted to rule out a rise in VAT but Mr Darling judged that irresponsible. With hindsight, the nods and winks that Labour would not increase VAT were not enough and the Tories were let off the hook.

Many Labour figures share Mr Brown's instincts. David Miliband was brave to stick to the Darling line when it would have been easier to go with the Labour flow running strongly against the new Government's cuts.

Similarly, it might be tempting for the new Labour leader to oppose every cut. Labour has drawn neck and neck with the Tories in recent opinion polls and may well enjoy a comfortable lead after the headline cuts for each Whitehall department are announced on 20 October. The party got used to winning elections under Tony Blair and might soon convince itself the next one is in the bag. Everyone wants to "move on" from the Blair-Brown era but they shouldn't forget how much gruelling spadework was done by New Labour – crucially, on economic credibility.

With the Tories and Lib Dems locked in embrace as they wield an unpopular axe, the new Labour leader might think he couldn't possibly lose. He might be tempted to carry on attacking Mr Clegg and his party, who have become hate figures for many Labour folk for sleeping with the Tory enemy.

Yet the polls may prove misleading. While the Coalition's ratings are slipping, David Cameron and Nick Clegg remain popular. The new Labour leader will have to compete with them, look into the eyes of the public, see what they want in their lives and make sure Labour gets real.

Voters may fear the cuts but they know the deficit must be reduced. Wiser Labour MPs have got the message in their constituencies. "People blame us for leaving the mess behind," one admitted. The global crisis was not made at No 10 but Labour will lack credibility unless it admits the need to learn lessons.

YouGov polling published today by the Demos think-tank suggests Labour is out of tune with mainstream opinion. Voters who backed Labour in 2005 but deserted it this year are more likely than those who stuck with Labour to regard reducing public spending as a priority and less likely to regard the state as a guarantor of public services.

"Labour has lost the political centre ground and will struggle at the next election without a shift in political positioning," said Richard Darlington, head of the Open Left project at Demos. "Labour's next leader needs to show it is prepared to cut public spending, that it doesn't think the state is the answer to every problem and that it is prepared to protect low-paid workers against the insecurity that comes with globalisation."

Labour will not regain power if it pretends that money grows on trees.