Quincy, IL? Reno, NV? Cheyenne, WY?
ROFL This guy uses the Star Trek font, clearly has no idea about network planning, yet this is the vision that captivates America. Any publicity is good publicity, I guess...
The problems have been listed elsewhere, but
A) it's extraordinarily difficult to build between Denver and Las Vegas. That's why the transcons didn't do it and the interstates took 40 years to finish the route (Glenwood Canyon, San Rafael Swell, etc - not easy terrain).
B) high speed rail is not time-effective for trips of this length. Individual journeys between cities along the route might keep things profitable, but the huge unpopulated areas of the Great Plains and the Mountain West mean that transcontinental lines don't make sense unless we can double speeds using a maglev or something. Chicago-New York is about as long as we can get, and even there, most travelers would still choose to fly. The seats would be occupied instead by people traveling to/from intermediate cities. This is why HSR plans are being developed in regional networks instead of a national one.
C) this map seemingly picks segments randomly from the existing Amtrak map, regardless of what makes sense in a national network. Tiny cities like Quincy and Reno don't need HSR spurs. Not every line needs to pass through Chicago, either... a cutoff from Springfield to Indianapolis would enable a variety of other city-to-city trips within the Midwest.