The simple present is OK, and also "will + verb." With the verb "suffer" it would be more idiomatic to use the progressive:
"” It won't be long before we're suffering from a shortage of water,"
...which highlights the situation of being without water. (It's also more idiomatic to say "a water shortage," unless you are referring to a shortage of a certain kind of water, e.g. drinking water or water for a particular purpose.)
This construction (also "It won't be long UNTIL...") allows a variety of verb forms. Examples from Google:
"” Consequently your child may be surrounded by an endless supply of crisps, chocolate and fizzy drinks. The pressure to conform can be very difficult for youngsters and unless you can come up with a variety of appetizing goodies it won't be long before your child starts to bemoan his lack of junk food. (Simple present)
"” It won't be long before individual investors are paying pennies rather than dollars to trade stocks and bonds. (Present progressive, which is especially common.)
"” I should also note that when people begin accepting the notion of "benign" worms, it won't be long before someone will release a malevolent worm bearing a benign worm's signature. (WILL-future)
"” It won't be long before you will be paying more for your policy than if you had simply included the inflation protection in the original premium. (Future progressive, also common)
"” "It won't be long before young couples are going to have to hire someone to watch their kids so they can both work." (GOING-TO future)
"” Winsome will settle down soon enough and it won't be long before she will have taken over the whole household, found her favourite place to sit, sorted out how far she can go with the cat, and covered the floor of the lounge with her collection of soft toys. Puppy heaven! (Future perfect)
The choice of verb form often depends on whether the verb represents a single action, a state, an activity, or general habit.