This really comparing apples and oranges.
HSR will grow between the major clusters of cities, such as the NEC, around Chicago, in California and in the longer term in Texas and Florida - all of which have clusters of big cities some hundreds of miles apart. In those situations, HSR can be a viable alternative to both driving and air (and to be economically viable, HSR must abstract passengers from both segments). Passengers may accept train trips that are 1 to 2 hours longer than the equivalent flight, taking into account the simpler checkin and less security hassle. So that means trips of maybe 300 or 400 miles are on the radar. Beyond that the economic case gets very thin.
LD trains cover thousands of miles. HSR can never be so fast as to get at the airlines throats on those journeys, and as HSR lines come with a pricetag that scales with the length of line to be built, those are going to have far higher start up costs and comparatively lower revenue streams.
I do however see a risk that uninformed decison makers may seen HSR as an excuse to divert LD funds.
The USA is today probably the premier country for LD trains. Russia, India and China have them too, but apart from that there aren't many left. Most of the European LD routes have been fragemented precisely because of HSR and railways seeking to eliminate in-house competition to their own HSR. Until about 10 years ago there was still a direct train from Paris to Bukarest and a bit before that there was a through sleeper from Lisbon to Vladivostock. All that is history and if you want to do those trips today you'll have to change trains several times (and use plenty of HSR)
In the sense of train operation it is apples and oranges. LD's and HSR corridors fulfil totally different transportation needs.
But in terms of transportation politics this might be the choice the US has to make anyway, as it might not be possible to get funding for both. Even if we leave out operating subsidies at least it is a choice in terms of needed investments to maintain/enhance LD routes or building up new HSR or semi-HSR intercity corridors. Or more concrete, spending the hundres of millions needed for a daily Sunset Limited or maintaining the Raton Pass route, or putting them into corridors like Chicago - St. Louis. It will be hard to get a political coalition to do both.
One thing that will for sure not happen is true HSR from coast to coast. If the huge investments in new ROW has to be warranted, it has to be high volume corridors of a distance, where the train will become the preferred mode of travel for a large part of the market. On transcontinental routes any ever so fast train will still spend far, far longer than a plane, and will only pick up a fraction of the market. There will (and should) never be HSR tracks from Chicago to LA.
In the best of worlds a good number of HSR and enhanced intercity corridors all the way down the east coast, in the Mid West, Florida, Texas and California and maybe a few other places could be combined with a skeletal LD network like today. But it requires political will to keep funding both, both in terms of (large) investments and in therms of operations. Some HSR and intercity routes will be profitable, others not and the LD's probably never.
But if choosing is necessary, good HSR and intercity service in feasible corridors will transport much more passengers much more miles than the LD's and do much more for congestion, energy saving and the environment in general. Even if the choice is painful.
As Cirdan notes this is pretty much the choice Europe has taken - not because the railroad companies saw transcontinental routes as competition to their HSR's though, but simply because they largely are not competitive with any mode of travel, and the political choice has been to focus money and interest on mass transportation in corridors. This has happened also in the countries that has not invested in HSR (like Denmark, where I reside). Part of the reason is also here that the railroads are run on a national level and not by the EU or any other transnational entity, and there is very little pressure to get a train from Copenhagen to Rome, but lots of pressure to get better service on the short distances across the country or to the nearest large cities in neighboring countries, like to Hamburg in North Germany.
Consider this .... (specially in the context of Shanghai) 
