So AmTrak is a terrible system for long distance travel in the US. It's too slow compared to flying, has to compete with freight traffic, and it can't compete with the value of driving for comparable distances.
So, let me propose an alternative; the maglev. Although construction of maglev infrastructure is incredibly expensive, it typically has lower operational costs than traditional rail, and can operate at significantly higher speeds. For a region like, say, the Midwestern or Southern United States, where a route would only have stops every ~50 miles, a maglev system could make a business case. For trips between 300 and 500 miles, which are just short enough to justify flying, it would save the 2 hour security check, and if averaging ~150mph (conservative for most systems of its type) a maglev could realistically be closing in on its passengers' destinations by the time an air traveler would be seeing the wheels leave the runway.
The massive downside is, naturally, the lack of maglev infrastructure existent in the US currently, but there are several routes that could make a case even in the current market. My immediate thought would be Pittsburgh-Atlanta with stops in Nashville, Louisville, Cincinnati, and Columbus; maybe include a Cincinnati-Chicago line with a stop in Indianapolis.