I think that's one of the first scenarios for which one should be prepared. How long you can survive in your own home without assistance or outside support is going to be determined by the weakest links in your chain and the hardest for which to find a substitute.

As a resident in a NY high-rise, I know water and warmth are likely to be my weak points. I have enough water for a while, but space limitations make it difficult to store a lot more. If I had to remain here for days on end with no power and heat, then I would need to make some serious adaptations. I would need to make something like tents inside our apartment, and we would need to dress warmly. Not much else we can do because we have nothing in which to burn any wood or other fuel, except maybe a candle or chafing fuel. My only other option is to move, and we are soon. I have enough food to last more than a month stashed away.