What has happened is that they have more voters out of work than in work
That is not the case. Denmark's 5.5 million population includes children and people who have retired. Denmark has 4.1 million registered voters (a figure which, of course, also includes young people at university) of whom roughly 2.3 million are working and around 1.2 million are retired.
It is true that less than half the total population is working but that is not unusual. It is also the case in many other countries, including the UK, due to the number of children, students and retired people.
The figure of 1 million workers in private enterprise also appears to be wrong. According to the statistics I've found the true figure is 1.4 million.