There is a law here in the United States, and the law says you can't over stuff the car. For example if the car only has 4 seat belts, only 4 people are supposed to be in the car. It doesn't matter if you can fit 6 people in the car, it's illegal and you can get a big fine. With that being said, since Americans like big families(and most American families are big families) they need something bigger like a 7 passenger SUV or a mini-van. Also, since the economy is better here, people don't care so much about gas mileage. Parking is not a problem here, so people don't care about that either. Also a big car is safer. Another problem is, Americans are bigger than Europeans(size wise, they are taller,more fat etc.) so they need more space. Most places in America have bad weather(like lots of snow) so people buy a big car because it will handle better on bad weather conditions. Americans also like to go on dirt roads(some consider it a hobby), mudding (another hobby) and camping. For all of these activities, a SUV, minivan or truck would be better because it will handle better. There are just lots of reasons, some of them I can't think of right now.
As for your real question, no Americans are not willing to buy small cars. Sub-compacts(the car types you're talking about) do exist in America, and there are some really nice ones like Ford Fiesta but people are not willing to buy them. It's too small for Americans. They sell, you can see them, but it's rare to see a sub-compact car here. However there are lots of compact cars like Honda Civic,Toyota Corolla,Ford Focus etc. However most of the vehicles on the road are SUVs,trucks and mini-vans. This makes it very risky for someone to buy a sub-compact car, because if you get hit by the big Ford F-150(#1 top selling vehicle in America for 35 years running), you would be lucky if you get out alive. It's just a big risk. Like I said though, Americans like their comfort. Also Americans like cars with big engines, because big engine=better performance. Not too many people care about fuel economy. For example the biggest Ford Focus engine in Europe is 100 horsepower, biggest Ford Focus engine in America is 140 horsepower.
I've never heard anyone buy a smaller car in United States because it's easier to park it. Most people who care about gas mileage are young people(high school students, college students, just out of college, newly married) and people who can't afford a big car(poor class). Middle-class and upper class people generally don't care about gas mileage. Generally, not always. There are lots of middle-class people who care about fuel economy and they buy cars like Honda Civic, Toyota Corolla and Toyota Prius, but most don't. I'm a college student and even people my age have big cars. Most of the cars are sedans but I still see lots of trucks and SUVs. Americans just love big cars.