The Tory leader set out proposals for companies to be given a £2,500 National Insurance break for every job awarded to someone who has been unemployed for three months or more.
While rejecting Gordon Brown's plan to increase borrowing to stimulate the economy as "irresponsible", Mr Cameron said he would not simply allow joblessness to soar.
Instead he urged the Prime Minister to adopt the Tories' £2.6bn tax break plan, which he said would fund itself by saving £8,000 in benefits for every new worker.
With Mr Brown laying the groundwork for an additional "fiscal stimulus" to stave off the downturn, the Government is expected to unveil its own tax cuts in the forthcoming Pre-Budget Report.
But the Prime Minister immediately dismissed the Tory strategy, insisting it was "not a funded tax cut at all" and that "the money is not there".
Mr Cameron drew the battlelines with Labour, warning that higher borrowing now would mean belt-tightening and tax rises later.
At a Westminster press conference, he said: "Having already maxed out one credit card, is it responsible for the Government to simply get another one?
"My answer to that is clear. It's irresponsible. It will saddle this generation and the next with a burden of debt that could take a decade or more to pay off.
"It means spending priorities shifting from schools and hospitals to servicing our debt. And irresponsible borrowing means more taxes on families and businesses in the years to come, putting a drag anchor on recovery."
The Conservative leader also insisted that a Keynesian-style "spending splurge" would not assist the economy in the long-term.
"All the evidence shows that trying to tackle a recession with a big spending programme doesn't work," he said.
Mr Cameron went on that funded tax cuts were a better response to the downturn than increased spending, arguing that they could be used to tackle rising unemployment, now close to 1.8 million.
He sought to strike a markedly different tone to previous Tory governments, which have viewed job losses as a corollary of economic recovery.
"The modern Conservative Party will not stand aside and let unemployment claim livelihoods and ruin lives," he said.
Mr Cameron made clear he did not agree with former Tory chancellor Norman Lamont's assertion that rising joblessness was the price to pay for keeping down inflation.
The Tory leader, an adviser to Mr Lamont in the early Nineties, told reporters: "It's certainly something I have never said, nor would I ever say."
He said that the Conservatives had introduced employment schemes in the 1980s, but action now had to be "bigger and quicker".
"What I'm saying is we have got to learn the lessons from history," he added.
The £2,500 tax break will be available for new jobs of more than 30 hours a week. For part-time work of 16 hours or more there would be a £1,250 break.
It will only be paid where the new-staff member has been on the dole for at least three months and pays only the basic rate of income tax.
To prevent abuse, only companies that make no redundancies for the three months before or after claiming the tax break would be eligible.
John Cridland, deputy director-general of the CBI, said: "While firms have to do what is right for their businesses in these challenging times, these imaginative proposals would help some small businesses keep people in work."
But David Frost, director general of the British Chambers of Commerce, said: "With unemployment continuing to rise sharply, companies are not in a position to think about recruiting new staff right now. Businesses are shedding staff.
"Cashflow is of primary concern to businesses at the moment. This policy announcement would have been a valid welfare to work initiative in better times, but it is not a survival tool for small businesses during a severe downturn."
The Federation of Small Businesses said the proposals were welcome but "could be bolder".
National chairman John Wright, national chairman of the Federation of Small Businesses, said: "Small businesses would be better helped by long-term reductions in National Insurance contributions rather than short-term breaks.
"There is a risk that encouraging businesses to employ those out of work for three months could provide a disincentive to take on those who are only just entering unemployment."
Employment Minister Tony McNulty scoffed at the Tories claims.
"There is no way they can get 350,000 new jobs out of these proposals," he said.
"There are too many restrictions being applied, the incentive is too small and many of these 'new' jobs will simply displace other people seeking work.
"In addition, the Conservatives just cannot pay for this tax cut - it is misleading of Cameron to say he can pay for getting the short-term unemployed back into work by using figures of savings you would make from the long-term unemployed."
Liberal Democrat leader Nick Clegg said: "To believe that this tax break would have anything other than the most marginal of effects on employment betrays the shallow level of economic understanding that the Tories have."
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