If you think about it, though, the dramatic growth of car ownership over the last sixty years implies that lots of families didn't have cars sixty years ago. Most of them didn't have horses either. Quite a few of them lived in suburbs or even in the country, but they managed to survive quite well. How?
The infrastructure was different, that's how. Many places that are car-dependent now didn't use to be. As Matthew Yglesias put it yesterday:
traditionally a great deal of walkable urbanism took place in small towns rather than in cities, and also in small cities [...] and “streetcar suburbs” rather than big cities.
For example, Westchester County had two more train lines that were torn up a long time ago: the New York, Westchester and Boston and the Putnam Line. You can tell where they ran just by looking for places that "feel like" the old suburbs. Visit Ardsley, or Heathcote Road in Scarsdale, and you'll know what I mean. Binghamton used to have regular train service, and Saratoga had much more frequent service than it has now, to a station right downtown instead of the current one.
"Joe from Lowell" commented on Yglesias's blog, "I like to use the example of the towns in old westerns. People walking up and down the street, saloons and banks and churches, apartments up above, houses on side streets, usually a train station nearby - but as small town/rural as anyone could ask for."
This has changed somewhat. The NYW&B went out of business in 1937 and the Old Put in 1958. The 2001 bankruptcy of the Grand Union supermarket chain hit a lot of towns hard across the greater New York area. Grand Union's distributor C&S sold off a lot of stores to drugstore chains and other buyers who had no intention of keeping the supermarkets open, and many towns found themselves with no supermarkets.
Even so, there are still many "streetcar suburbs" and cities that even today are walkable and transit-friendly. As far as suburbs go: in Westchester there are several places where you can live within a fifteen-minute walk of both a train station and a full-service supermarket, as well as a range of shops and restaurants. Examples include Bronxville, Harrison and Tarrytown. There are similar towns in New Jersey (e.g. Montclair) and Long Island (Rockville Centre). Parts of New York City itself have a pretty suburban feel, but are still close to shopping.
Similar situations exist in medium-sized cities like Binghamton, large towns like Saratoga Springs, and small towns like Red Hook. Even in relatively car-dominated areas, there's often a significant percentage of the population that manages to live car-free. In many of those cases, unfortunately, even if you can find a house that's within walking distance of a supermarket there aren't many jobs that are within walking distance of such a house, and many desirable shops or restaurants are in unwalkable locations.
Overall, it's a lot easier to live without a car than some might suggest, and it's a lot easier to serve the populations of medium-sized and small towns than some might claim. All you need to see it is a little imagination.