The Chancellor's trust rating plummeted after he was accused of presiding over a "millionaires' Budget" last month with a cut to the 50p top tax rate next April.
A clear majority of voters questioned by Comres for ITV News also said they lacked faith in the Prime Minister's abilities.
The political turmoil of the past few weeks has seen the proportion who back Mr Cameron on the economy hit a new low of 31%, down from 36% last month.
In addition, 53% do not trust the Prime Minister's ability to steer the UK through turbulent economic times. This equals his worst rating.
Trust in Mr Osborne was even lower, with voters backing his abilities on the economy at 21%, down from 25%. Those who did not trust him with the nation's purse strings rose to 60%, up from 52%.
However, there was little comfort for Labour in the poll of 2028 people between March 30 and April 1. The findings show Labour leader Ed Miliband struggling to capitalise on the Coalition's many problems.
Mr Miliband's approval rating rose just two points to 18%, while Shadow Chancellor Ed Balls's stalled at 15%.
Fewer than one in five people back Mr Miliband's plans for the economy, although that figure was up slightly on last month.
The slump in Mr Cameron's ratings follows a public backlash over the administration's so-called "granny tax" on pensioners' incomes, the impact of cuts on families, the Tory donor scandal and advice, which backfired on the Government, that motorists should stockpile fuel before a threatened strike by petrol tanker drivers.
Good Friday was described as "Bad Friday", because of tax changes that came into effect yesterday. These left many families financially worse off.
Those with children will lose an average of £511 a year and some may lose up to £4000 worth of working family tax credit.
The Coalition's opponents seized on the poll, with the SNP branding the findings devastating.
Labour's Shadow Scottish Secretary, Margaret Curran, said the findings were to be expected given the impact on thousands of families of tax changes introduced in the last Budget.
She said: "This will come as little surprise to working families across the UK who are being hammered by the Government.
"Today is the first day when 84,000 families in Scotland will go without all their tax credits. This Cabinet of millionaires is hitting pensioners and families on middle and modest incomes to fund huge tax breaks for the very wealthiest. It is deeply unfair, deeply regressive, so no surprise it is also deeply unpopular."
She also criticised Mr Osborne for a Budget that was "unravelling by the day".
Stewart Hosie, the SNP's Westminster finance spokesman, said: "This is a devastating poll, but it is no surprise trust in Tory economic policy
has collapsed. After their complete incompetence in creating unnecessary panic at the petrol pumps, their Budget for millionaires, and absolutely no sign their discredited economic policies are producing any upturn in the UK economy, everyone can now see the Tories are unfit to govern."
The Coalition has struggled to get on the front foot since last month's Budget. The "granny tax" resulted in the Chancellor making a £3.3 billion raid on pensioners' allowances, leading to accusations that millionaires were benefiting at the expense of the elderly.
This was followed by the Budget announcement of a tax planned for hot takeaway food such as pasties, and Mr Cameron suffering a humiliating PR disaster over when he had last eaten a pasty.
Critics also claimed drivers, already hit by a Budget commitment to keep to previously announced fuel duty rises, faced panic at the pumps as Ministers told them to fill up ahead of a strike that has yet to be called.
Cabinet Office Minister Francis Maude also suggested people fill up jerry cans with fuel at their properties.
Moreover, the Prime Minister was forced to release details of private dinners held at Downing Streets and his country retreat, Chequers, with major donors to the Tory party.