This is sort of my dream, but every time I've checked prices they have been astronomical, upwards of, say, $800 to go from Emeryville to Florida (just a regular coach seat).
A lot of American friends were surprised we were doing this - they had this idea that it would be uncomfortable and boring. They just couldn't have been more wrong. Between the comfortable room-ette things, often very friendly and varied fellow travellers, surprisingly tasty food and absolutely amazing scenery, it's a fond memory.
Of course, we scheduled in plenty of time - if you need to be somewhere punctually, Amtrak is not really your best bet.