He urged activists to stick with his leadership, saying “hard work” and “strong families” would ensure the country weathers the storm.
He said: “These are difficult times. We are being tested.
“I can’t tell you that all is well, but Britain is on the right track.”
His speech comes the day after the International Monetary Fund (IMF) said the UK economy would shrink 0.4% over the course of 2012.
Cameron told the conference: “Unless we act, unless we take difficult, painful decisions, unless we show determination and imagination, Britain may not be in the future what it has been in the past.
“Because the truth is, we’re in a global race today. And that means an hour of reckoning for countries like ours. Sink or swim. Do or decline.”