Is it possible to measure happiness?Critics say the £2m (20m yuan) scheme will not produce any meaningful results. Others suggest it is unwise to carry out a survey into the nation's happiness just as the government launches the biggest public spending cuts in decades.
Mr Cameron himself admits that it is easy to brand his scheme "woolly" and "impractical", but it is not without precedent.
Canada has an Index of Wellbeing which looks at how things like money and education affect health and the sense of community. And the Kingdom of Bhutan has used its index of Gross National Happiness (GNH) since the early 1970s as a tool to help policy-making.
So what kind of answers is he likely to get? While the full survey begins later this year, respondents to an initial consultation have already listed their top priorities.
Job security, good health and relationships with family members are what matter most to people in the UK, according to the findings. In fact, having a job was listed as more important than being paid a high salary.
So perhaps there is truth in the old adage that 'money can't buy happiness'. An idea David Cameron may find solace in as he tries to find a way out of the recession.