Historically, the most common means of long term water storage was the cistern. This is precisely what was done during the 19th century with many Midwest households; a handmade brick cisterns was sized to last months between rainfalls for one household.
Now, for long term planning, cisterns of many different sizes are available, along with pumps and accessories for treating the water while in the tank.
Modern Underground Cisterns With proper planning, one could easily store enough water in a cistern to last months (depending on your regional annual rainfall and the size of the household), or, you could use the cistern in-line with city water.
Cistern Technology Planning a cistern in new construction plans might be smart. In rural areas where pump capacity is low, cisterns can add not only volume but pressure to a system. One could retrofit this technology to an older home or, like my place, you may have an abandoned (but still functional) cistern somewhere buried in your yard.