What will be interesting is how local governments and social agencies will respond. In New England's poorly insulated houses (many built in the 1920s) with oil furnaces, it is not unusual to go through 200 gallons of oil per month in the winter, which at $5 a gallon is quite a bit of money for those in the social class that typically lives in row houses.
But there are also some pretty tightly knit communities, many the remnants of previous generations of immigrants (e.g., Swedish, Polish, Italian, etc.) and recent immigrants (many from South America). It is not difficult to envision a support system within these communities that could help the most needy. For example, in floods and in the Blitz, people gathered and slept in school gymnasiums. If heating fuel becomes a crisis of that proportion, people will gather and sleep in the gym.
Certainly some people will die in the transition, particularly if they are not connected to their neighbors, but the question is about the scale of the problem.
Here is my simplistic approach:
