800 mile triangle is about 250-300 miles per side. You wouldn't need TGV level speed (180mph) for that to be effective. You could run trains at an average of 100-125mph, which is not much above current levels in the northeast (BOS-WAS expresses average about 80, on a route with little significant capital investment since 1939) and still have an extremely competitive service, at much much lower constructions costs.
It would still be a big project...but the economics would work much better if you aim for 2-3hr journey times instead of 1hr30.
I'm not sure you can simply improve the current infrastructure and buy some Pendolino-type stock - many of the lines in Texas are actually single track, currently used by freight trains, presumably some of it coming up from Mexico. My guess would be there's a lot of bridges to widen, second lines to lay and a big electrification project. What do you do with the existing freight? Mixing very low speed freight on a line like that in the North East corridor would be difficult.
Also the more the total journey time gets stretched the less attractive rail becomes, and even at the 1hr30 level the trains would have to go right into DFW etc to make any sense considering that a lot of the current air passengers are actually connecting onto another AA flight.
All-in-all I think there are probably better candidates for such a scheme in the US.