Outside of the NEC, California, Florida, Texas, and the areas within approximately 200 miles of Chicago
You've just described probably 80-90% of the US population. If they can benefit from it, it will happen.
It is worth remembering that no one builds HSR for people who live in the sticks, even when the tracks actually pass through the sticks. Even when stations are built in the sticks they turn out to be not so successful. Considering that a majority of US population lives in urban or suburban areas (say within 200 miles of the major urban areas) and not in the sticks, it is hardly a valid argument to say that HSR won't work because the area of US has a lot of sticks area.
Well, if you get the NEC, FL, TX, CA, and IL/MI/IN/IA/MO on board, that's probably enough. The key is FL and TX, really:
The NEC has 82 CDs (I include MA, RI, CT, NY, NJ, PA, DE, and MD here). CA has 53. IL has 18, IA 4, MO 8, WI 8, IN 9, MN 8, and MI 14, for 69 total. TX and FL add 63. Without Texas and Florida, you only have 204 seats. TX and FL adding 63 gets you to 267, which gives you room to maneuver and drop off Congressmen from rural parts of these states (say, Western PA or northern MI).
As to the urban/rural bit, there's the sticks and there's the sticks. "Real" HSR to/from Salt Lake City will probably run into some hard-and-fast limits due to the mountains, and you can't really justify a line in the Boise area based on what I suspect the travel rates will be. There are also lots of cities that you'd really need to spend time rebuilding service for a few years before I think you could justify pouring a billion dollars into a higher-speed rail link. Simply throwing in a line from Chattanooga to Memphis is a recipe for explaining why we just spent a lot of money on an underused line...not just because the line does not exist as a service now, but because you rarely get a market out of nowhere that would justify that kind of spending.