The fact that a greater share of the dependents will be elderly rather than children will put an additional burden on society's resources, as the elderly consume a relatively large share of per capita resources, whereas children consume relatively little.
This inevitable drop in the growth rate of per capita GDP relative to the growth of productivity could be cushioned by an increase in labor force participation, which would boost the ratio of workers to population. Increasing labor force participation seems a natural response to population aging, as Americans not only are living longer but are also generally living healthier.