In a keynote speech on the economy, the Prime Minister accused Labour of "reckless" spending and said the public sector had to be brought "back into line".
If drastic cuts were not implemented, the Treasury would be spending an annual £70 billion on debt interest within five years - more than on schools in England, transport, and fighting climate change put together.
Speaking alongside new Treasury Chief Secretary Danny Alexander, Mr Cameron told an audience in Milton Keynes that now the Tory-Liberal Democrat coalition had been given access to the books, it was clear that the "overall scale of the problem is even worse than we thought".
"How we deal with these things will affect our economy, our society - indeed our whole way of life," he said.
"The decisions we make will affect every single person in our country. And the effects of those decisions will stay with us for years, perhaps decades, to come.
Video: PM: Deficit worse than thought
"It is precisely because these decisions are so momentous, because they will have such enormous implications, and because we cannot afford either to duck them or to get them wrong that I want to make sure we go about the urgent task of cutting our deficit in a way that is open, responsible and fair," he said.
"I want this Government to carry out Britain's unavoidable deficit reduction plan in a way that strengthens and unites the country.
"I have said before that as we deal with the debt crisis we must take the whole country with us - and I mean it.
"George Osborne has said that our plans to cut the deficit must be based on the belief that we are all in this together - and he means it."
Mr Cameron went on: "Based on the calculations of the last government, in five years' time the interest we are paying on our debt is predicted to be around £70 billion. That is a simply staggering amount...
"Today we spend more on debt interest than we do on running schools in England. But £70 billion means spending more on debt interest than we currently do on running schools in England plus climate change plus transport.
"Interest payments of £70 billion mean that for every single pound you pay in tax, 10 pence would be spent on interest."
The Premier stressed that the UK's position was better than that of Greece, which has been left in financial and social turmoil in the wake of the credit crunch.
But he added: "The global financial markets are no longer focusing simply on the financial position of the banks.
"They want to know that the governments that have supported the banks over the last 18 months are taking the actions to bring their own finances under control...
"Around the world people and their governments are waking up to the dangers of not dealing with their debts.
"And Britain must be part of that international mainstream."
His comments come as ministers prepare the ground for the emergency Budget on June 22, when Chancellor Mr Osborne will try to make serious inroads into the £156 billion annual deficit.
Tomorrow Mr Osborne and Mr Alexander will publish the principles meant to underpin both the Budget and the spending review which will come later in the year.
The Government is desperate to persuade people of the need for what it calls the "difficult decisions" it is set to take and will hold a public consultation on its plans.
Mr Cameron said if action was not taken immediately the "best case scenario" was "increasingly punishing amounts of interest on our debt", and interest rates could also be forced up.
He insisted people recognised that the financial crisis was "Labour's legacy", accusing the former government of being "far too hostile" to the private sector, while wasting money in the public sector.
The boom of the last 13 years had been built on immigration and growth in the financial services that was partly "illusory".
"Nothing illustrates better the total irresponsibility of the last government's approach than the fact that they kept on ratcheting up unaffordable government spending even when the economy was shrinking," the PM said.
"It really has been a tale of two economies. A public sector boom - and a private sector bust.
"So while the people employed by the taxpayer were insulated from the harsh realities of the recession everyone else in the economy was paying the price.
"And now we're all paying the price because the size of the public sector has got way out of step with the size of the private sector.
"We're going to have to get it back in line - and that will be much more painful than if we had kept things properly in balance all along."
TUC General Secretary Brendan Barber said: "The Prime Minister says that cuts that will affect every single person in our country, but deficit reduction through cuts alone will inevitably hit the poor, the vulnerable and the great mass of middle income Britain who depend on public services. Those at the top will hardly notice.
"At the same time he is hinting at a retreat on modest measures to reform capital gains tax that ask the better-off to make some small contribution. It is hard to see any fairness agenda here."
Dave Prentis, general secretary of Unison, said: "This was a chilling attack on the public sector, public sector workers, the poor, the sick and the vulnerable, and a warning that their way of life will change.
"There was nothing in this speech that told the rich, the banking and financial sector or the City speculators that their privileged way of life will change.
"With breathtaking gall, David Cameron is spinning a myth about a hard-done-by private sector. The Tories and their friends in big business seem to forget the tens of billions of pounds of profit made by the private sector out of public sector contracts."
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