To do this, I looked at the Department of Statistics' Household Expenditure Survey. The Survey has data on income and expenditures for different income groups. For each group, we can examine what proportion spend more than they earn.
The results are shown in the graph below. Here, we have the proportion of Singaporean households spending more than they earn, grouped by household income. Understandably, richer households are less likely to over-spend than poorer ones. Only 3% of households earning $7,000 to $9,999 are overstretched, compared to 25% for households earning between $1,000 to $1,999.
Note: I excluded those earning less than $1,000 as it includes retirees, as well as those earning more than $10,000 due to data limitations.
This was higher than I expected, but is this really a problem? On one hand, it might be a matter of personal irresponsibility, which PM Lee alluded to. On the other hand, it could be something in economics called "consumption smoothing", where the young, expecting incomes to go up as the rise in seniority in the workplace, spend more today and save more in the future. We can only guess.