The US is designed differently than the other heavily developed areas of the world. It's not about being "too big" or "not dense enough", it is more complicated than that.

The Northeast US has a similar statistical density as areas of Europe but looks so much physically different. Take some time on Google Earth and check it out. There is a nonstop blob of suburbs that go almost all the way from DC to Boston. In a proposed train network, most of the population has a long trip to the central station before they can take the train to the other city. They still need a car, and need somewhere to park it. In Europe or Asia cities are more concentrated, and the countrysides are less populated.

Building a center-city to center-city train network in the US is not impossible, but it simply wouldn't be as efficient as it would be in Europe or Asia because of the way the cities are designed.