No one wants to work more when they are old. People want to retire and collect retirement benefits so they do not have to work anymore. The government should make sure that there is funding for Social Security so that workers do not have to work past the current retirement age.
Workers do not want to work longer to save more money because they already have little faith in the benefits of the future and how long they will last. People would rather retire earlier, knowing they can still work further. If they want to already start collecting their benefits, that's their choice.