It seems unlikely that the river would suddenly dry up, the risk is that some accident or attack would render the city water supply unsafe to drink.

Surely in such circumstances, the water could still be supplied and used for toilet flushing, and probably also for laundry and showering.

The much smaller volumes of water needed for drinking could probably be supplied in bottles or cans by the TPTB. It would of course be prudent to have ones own reserve of water rather then being reliant on the authorities whose response might be found wanting.

If I lived in the area I would equip myself with enough bottled drinking water to last say a month, and would if possible also store perhaps a hundred gallons of non drinking water in drums or barrels.