The average person in the US uses about 80 to 100 gallons of water per day. Of course, just to survive, he or she would need vastly less than that (mostly for cooking and drinking, a little for washing and rinsing wounds). A person can of course survive for years without bathing or showering. Indirectly, the average consumption rate is a lot more -- about 2000 gallons. Food production accounts for about 90% to 95% of that, but again during the months and years right after a massive nuclear attack, the survivors of the attack can obtain most of their protein and calories from food grown before the attack. So, you can sustain a "population center" on rainfall, ground water and surface water especially of the members of the "population center" can relocate if they find themselves in a place (Phoenix AZ?) where there is not enough water to go around.
Fuel is similar: the amount currently used by the average person is much higher than the amount needed (i.e., to transport food and other essentials) just to keep people alive until our industrial base can be reconstituted enough that survival becomes easy again, so we can expect to be able to survive for a few years on fuel that was produced before the attack. Most motor vehicles will probably survive the attack, for example, according to analyses made by US war planners during the cold war, and the fuel tanks of each of them will on average be about half full even if no warning of the attack reaches the general public. Home heating is not strictly necessary for survival except maybe on the coldest nights of the year, which is good because I doubt there is enough firewood in the continental US to keep the survivors of the attack warm every night for a few years.