The problem isn't that it can't happen, the problem is people won't vote to pay more in taxes. Left or right, we've shown that any candidate that runs on increasing taxes gets slaughtered because the voter base is too short sighted. New rail is incredibly expensive, taxes would need to be increased to pay for it (the money HAS to come from somewhere).
It's "functional" in that people can get from Chicago to NYC relatively quickly - through a flight. Sure, it's gonna cost a few hundred $$ a person, but it's not enough of a barrier to get people to pay significantly more in taxes for a few years to pay for an alternative.
The federal government isn't going to step in and do something like this ever either. They're the only ones who could even conceivably do this, but spending billions for 2 specific states doesn't sway voters from the other 48.