It's unlikely that you'd be able to push trainsets above 220mph or 350 km/h in revenue service. Even then, the actual average speed for a Chicago-NYC run would be closer to 160mph, since you'd have to make some stops along the way, and there's no way you're maintaining 220 in the Appalachians. The shortest plausible route would be essentially the turnpike route (parallel the NJ, PA, OH, and IN turnpikes in a NYC-Philly-Pittsburgh-Cleveland-Chicago route), which is going to run about 800 miles or so--or about 5 hours. More importantly, you can't shrink the project to a smaller viable project--not connecting Chicago and NYC is going to give you a losing line, and not hitting that top speed is going to be too slow.
And Chicago/NYC is the "easy" connection. Atlanta, Texas Triangle, and Florida are simply too far away, let alone trying to reach across the Plains to hit Denver, Phoenix, and Las Vegas en route to LA/SF.
Well in other places, the HSR just tunnels through the mountains. Rome to Bologna, which is a comparablyish distance to Harrisburg to Pittsburgh is a good example. Highish speed rail already exists between NYC and Harrisburg and Pittsburgh-Cleveland-Toledo-Chicago is comparably easy (especially if you can use the already-electrified SSL tracks to get in Chicago).
By my count, a NYC-EWR-PHL-HAR-PIT-CLE-TOL-SBN-CHI train would directly serve metros with ~50 million people (and indirectly serve much of the rest of the northeast and midwest).
Realistically, your problems start between roughly Youngstown and Harrisburg. Between Harrisburg and Altoona, the terrain is ridge-and-valley, which means the tradeoff is twisting to follow a water gap or punching a small tunnel through the ridge. West of Altoona, the dissected Allegheny Plateau begins, but you have to first make an 800-1000 foot climb to reach the plateau, which means in practice a ~7mi, 2% grade tunnel. From thence to around Youngstown, you're on a dissected plateau, which means every water course (for whom the idea of a straight line is anathema) has carved a gorge. It's a rather different situation from just tunneling through a massif.
Sure, you can fix issues with tunnels and bridges. But that doesn't come cheap. And what is by far the most expensive portion of the line is the part that's necessary for any sort of traction, which greatly increases the chances of the entire project being a white elephant (keeping in mind, again, that even in the best-case scenario, you're still at the very margin of being able to run a profit). The economics look worse than the Turin-Lyon HSR, which is already criticized as an expensive, unnecessary boondoggle.
And Chicago/NYC is the "easy" connection. Atlanta, Texas Triangle, and Florida are simply too far away, let alone trying to reach across the Plains to hit Denver, Phoenix, and Las Vegas en route to LA/SF.