I would very much like to be able to get from Boston to California by sleeping car in about 24 hours or less. TGV technology ought to make something like this possible.
However, it's unlikely that a high speed track all the way across the country is going to be funded purely to run sleepers. On the other hand, most travelers who have a bit of experience with trains seem to find that if their trip happens to be doable in about 3 hours or less by train, the train is a better choice than the plane. So I've been looking at the question of whether you can build a lot of these track segments which individually will make sense to the average airplane traveler, which will happen to connect to each other for the convenience of the long distance train traveler.
If we as a country were to collectively decide that where a major city is within about three hours or less by high speed train of another major city, that building TGV quality track makes sense, I believe it is possible to come up with a route that goes all the way across the country by high speed train. I'm assuming that the train will average 170 miles per hour from station to station, and that the major cities that can be considered are the top 30
US Combined Statistical Areas.
Where I've used track miles, they come from the Amtrak timetable; a high speed route might end up being a little shorter. Where I've used highway miles, the numbers are a bit rough, in that I've gone with whatever Google Maps thinks is the city center to be used when an address within the city is not specified, and a track route might not follow a highway route at all. Still, a rough estimate is better than no data.
The times between Denver and adjacent cities are a bit on the long side; then again, the Denver airport has managed to make itself huge to help keep itself competitively slow with the extra travel time those trains encounter relative to the rest of the train segments on this list.
One possible routing:
Philadelphia is the 8th largest Combined Statistical Area.
Philadelphia to Pittsburgh is 353 track miles on the current route; that trip would be roughly 2 hours at 170 MPH.
Pittsburgh is the 18th largest Combined Statistical Area.
Pittsburgh to Cleveland is currently 140 track miles, which would be under an hour at 170 MPH.
Cleveland is the 15th largest Combined Stastical Area.
Cleveland to Chicago is currently 341 track miles, which is right around 2 hours at 170 MPH.
Chicago is the 3rd largest Combined Statistical Area.
Chicago to St Louis is 297 highway miles, a bit under 2 hours at 170 MPH.
St Louis is the 16th largest Combined Statistical Area.
St Louis to Kansas City is roughly 250 highway miles, roughly 1.5 hours at 170 MPH.
Kansas City is the 22nd Largest Combined Statstical Area.
Kansas City to Denver is 603 highway miles, a little over 3.5 hours at 170 MPH.
Denver is the 14th largest Combined Stastictal Area.
Denver to Salt Lake City is 534 highway miles, but that's a pretty indirect route. However, 534 miles at 170 MPH is a bit over 3 hours.
Salt Lake City is the 27th largest Combined Statistical Area.
Salt Lake City to Las Vegas is 420 highway miles, about 2.5 hours at 170 MPH.
Las Vegas is the 25th largest Combined Statistical Area.
Las Vegas to Los Angeles is 271 highway miles, a bit over 1.5 hours at 170 MPH.
And Los Angeles is the 2nd largest Combined Statistical Area.
There are some other possible variations on this theme. I was looking at Pittsburgh to Philadelphia because that's where the tracks go now, but Pittsburgh to NYP and Pittsburgh to WAS tracks might also be viable options for routes that would take less than three hours at 170 MPH. I think Pittsburg to Columbus to Indianapolis to St Louis is a viable option for meeting all of the basic criteria, but if not all relatively nearby large cities get high speed track connecting them, focusing on the very largest cities is probably best, even if that makes the cross country route a bit less direct.