Outlining his party's plans, Mr Cameron told BBC One's Politics Show: "We're not talking about swingeing cuts. We're talking about making a start in reducing our deficit.
"Look, if we have an election in May, your year is already under way... we believe, in proving we're serious about getting this deficit down.
"And those who say you're taking money out of the economy, I would say, if you don't do this, even more money could be taken out of the economy in two ways.
"One, because interest rates could go up as they have done in Greece. Secondly, money gets taken out of the economy because there isn't the confidence there and it's confidence we need so badly.
"People want to see a government that is taking decisions on a five-year horizon rather than with this government taking things on a five-week or, some say, even five-minute horizon."
'Albatross of debt'
Mr Cameron did not give a projected figure for cuts to public spending, but promised to work with the Bank of England to "make sure we keep low those interest rates".
"What year one [of a government] has to have is a start to cutting the public spending programmes.
"But it should be done in conjunction with the monetary policy authorities because we want to make sure that those interest rates remain low."
Return to strong, sustainable global growth is still some way off
Appearing on the BBC's Andrew Marr Show, shadow chancellor George Osborne said "early action" was needed on the deficit to avoid a "Greek-style budget crisis".
He insisted that it would be a "mistake" to wait until next year to begin tackling the "albatross of debt", as the government was planning to do.
However, Mr Brown used his weekly podcast on the Downing Street website to warn that the economy still needed support and that cutting too soon risked tipping it back into recession.
He said: "Return to strong, sustainable global growth is still some way off. So I can reassure you that we are not about to jeopardise Britain's economic future by suddenly pulling the rug from under the recovery.
"We will continue with the measures we have put in place that are supporting families and businesses and we will continue to invest willingly and whole-heartedly in this country's future - and I will make no excuse for that.
"Only with this radical approach and a plan for prosperity for all can we deliver renewed growth, jobs and opportunities for all."
Speaking on The Politics Show, Business Secretary Lord Mandelson said: "It is talking Britain down when David Cameron compares Britain ludicrously in everyone's eyes to Greece, and when George Osborne describes Britain as an exhausted runner at the back of a long marathon race unable to summon the strength to build our economy.
Vince Cable: "They've got themselves into a terrible muddle"
"That is disgraceful. It is irresponsible. It's also unpatriotic."
Lord Mandelson accused Mr Cameron of coming up with a "nice, attractive flow of soundbites", rather than concrete policies.
"What people want is a future prime minister who thinks clearly about the issues, who has perfectly sound judgement, who talks to people honestly about what we should be doing and comes up with policies that he stands by rather than wobbles around," he added.
Liberal Democrat Treasury spokesman Vince Cable said: "George Osborne and David Cameron seem to be at sixes and sevens on the crucial question of how the deficit should be addressed.
"The public must understand that we take the deficit very seriously. But it has to be addressed in a way that doesn't put us back into another round of recession, resulting in job losses and an even larger deficit.
"The time to cut the deficit is when the private sector is ready to take the lead in growth and job creation. We are clearly not at that point yet."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.