"But we've suggested that it could be at 4.44am. It's as good a guess as any, isn't it?''
Mr Dunstan said he did not know why people were so fascinated with symmetrical numbers.
"But as a demographer, it's just a good opportunity when these milestones come about to think about our population and how it's changing and how it's likely to change in the future.''
Mr Dunstan said only three factors contributed to population growth - births, deaths and migration.
"Given the births, deaths and migration that we've had since the last census, the estimates are indicating that that milestone will occur tomorrow.
"Currently natural increase - which is the difference between births and deaths - is the dominant contributor to our population growth. Net migration is relatively low at the moment.
"So given that, we suggest it's more likely to be a baby born.''
The landmark would be the second population milestone this year, after the Auckland population hit 1.5m in February.
But such symmetrical milestones are relatively rare. It was back in the mid-1980s when the population reached 3,333,333, and the population won't reach 5,555,555 for decades.
Population milestones are also quite fleeting - with growth of about 100 people a day, the population was likely to remain at 4,444,444 for only about quarter of an hour.
The milestone will put New Zealand's population close to that of Ireland, Croatia or the Australian state of Queensland, which reached 4,444,444 three years ago.
Statistics New Zealand's quarterly population estimates are based on trends since the last census.
Censuses are usually held every five years, but last year's census was delayed by the Canterbury earthquakes.
Mr Dunstan said the 2006 census was being used to produce estimates for further out than normal.
"The projections aren't designed to anticipate things like the earthquakes, and there's no doubt the earthquakes have had some demographic impacts, as our estimates have indicated.''
The next census on March 5, 2013 would be a "hugely important data source'' and be widely used by central and local government, businesses and communities.