Since George Osborne became Chancellor in May 2010, the 50p rate of tax has been a political headache. Instinctively a low tax Conservative, he has been unable to cut the top rate of tax because of his commitment to deficit reduction and the difficulty of justifying such a move as people across the country face unemployment and pay freezes.

The extraordinarily public negotiations over Wednesday's Budget over the last few weeks have shown that scrapping the 50p rate is high on the agenda. Last week, it was suggested it could be slashed as low as 40p. Today, the Telegraph reports that it is going to be cut to 45p from April 2013.

Osborne's argument is that the tax undermines investment and entrepreneurship. The government will cite figures which show that the tax has not raised as much revenue as hoped. When Alistair Darling introduced the tax in 2009, it was predicted it would raise £2.6bn, but reportedly the figure is in the hundreds of millions. Osborne will claim that cutting the tax to 45p could in fact raise more money as less people will avoid it.

It is difficult to see this flying with the public. The fact remains that this is a very popular tax: the polls have consistently shown overwhelming public support for the 50p rate. Last September, YouGov found that 59 per cent wanted to keep the tax -- including 50 per cent of Tory voters -- while just 23 per cent overall wanted to scrap it. A ComRes poll found that 48 per cent would like to see it raised to 60p, while 33 per cent did not.

Most Liberal Democrats are likely to be uncomfortable with the move, which is to be offset with a so-called "tycoon tax" aimed at preventing tax avoidance. Nick Clegg will insist that the "rich will pay more" after the Budget, while the increase in the tax-free personal allowance is expected to be speeded up. The tax threshold was due to be raised to £10,000 from April 2015, but Osborne could indicate that this will be moved forward a year.

Yet for all these moves to neutralise it, cutting the 50p rate, which only affects those earning over £150,000, remains potentially explosive. Stephen Williams, co-chair of the Lib Dem Treasury committee, told the BBC yesterday: "I certainly don't think that now would be the right time to announce the abolition of the 50p or the reduction of the 50p rate of tax. 2012 is going to be quite a difficult year for many families up and down the country."

As my colleague George Eaton wrote last week, the attack lines for Labour write themselves. Tax cuts for the rich are a difficult sell at the best of times. When the rest of the country remains mired in economic strife, it looks like a political impossibility.