In the UK, Virgin Trains cover the 200 mile distance from London to Manchester in about 2 hours (with the fastest express being 1:58), for an average end to end speed of 100 mph. And this is done on a railway that mostly runs on a 19th century alignment, and has a top speed of 125 mph, and which is shared with all manner of local commuter and freight trains.
In the US, that sort of speed would imply a travel time of somewhere around 4-4.5 hours for LA to San Francisco, 9 hours from New York to Chicago, 10 hours from Denver to Chicago. The latter two city pairs are particularly interesting: it's unlikely that high speed rail will be built over such distances, at least not anytime soon. But with enough incremental improvements, it's possible to get travel times down to a point where overnight trains are a reasonable option for getting across one-third of the country.