It seems likely that this "population decline" headline is slightly misleading. Even if deaths outnumber births, net immigration is likely to keep the total resident numbers rising slightly this year. Here is an article discussing the issues:
Conservatives eager to preserve what's left of Japan's "man at work, woman in the home" family model have been loathe to vastly expand the day-care system, for instance, for fear of encouraging more women to join the work force.
Another obvious possibility - loosening Japan's tight immigration laws to allow more foreigners to come here to work - has been blocked by a widespread distrust of outsiders and fear that foreigners would disrupt the country's social order.