We can do traditional catenary, but there's a risk of the high cost of US infrastructure eating up the budget.
Might be worth considering a hybrid system where you electrify the most busy corridors and then use battery-electric trains for much of the rest (but charged using a sort of overhead catenary), allowing you to reduce the amount of infrastructure significantly (but with locomotive capital costs to consider... including battery cars).
And yeah, once we have more experience with overhead high voltage heavy rail in the US, with upgraded commuter rail, we can then do HSR with some sort of rationality.
Because you only really need HSR between cities. In a city, you want good, electrified rail. HSR doesn't really do anything for city traffic (and could make it worse, actually, if not done at the same time as conventional rail upgrades).
In fact, Amtrak is not even necessarily better than flying. Amtrak gets like 56mpg per passenger, but airliners can easily get much better than that (particularly if you fly economy class): https://www.wsj.com/articles/SB10001424052748704901104575423... (and this article is using 2009 data... newer airplanes can get much better)
(This would be surprising unless you noted that Amtrak has low occupancy compared to airlines and has to maintain a lot of routes to underserved places and that trains have to carry a lot more weight per person because, in part, the trips are a lot longer... it's a bit better for short commuter trips)
So rail isn't even better for the environment than modern planes unless we electrify rail. (Which we need to do anyways, as we move lots of our cargo cheaply by rail.)