The 48 hours of battery would last a really long time as typically only about 12 hours will need to be used, thus you'd get very long cycle life. A battery used so lightly could get 10,000 effective full cycles, so probably would last multiples of 25 years from a cycle life perspective (calendar life may be another thing).
EDIT: If you add in geographical diversity and diversity in sources like wind, hydro, and geothermal, then you need to throw away a lot less energy and you need a lot less storage. IMHO, we should just bite the bullet and install a bunch of transmission lines (which could be done in 2 years, enabling us to decommission coal power within about 2 years in the US).