Now the question to this problem is, what can the government do about it?

One of the problem is that most women go for a career (I think this has been happening in most countries to for the past 20-40 years) so if they want to have a baby it means that they have to quit their job, and in Japan you can't just take a break for 1.5 year and then come back ( not as far as I know).

Than another things are, that Japanese woman marry later, because they don't want to give up their independence to raise children in an unhappy environment, or who, if married, decide that having children is a poor investment of their time and energies, and so refuse to bear them.