It may be a little sideways to compare Amtrak to freight hauling - though since most of Amtrak operations occur on freight railroads much of the cost gets mixed together. But maybe it would be better to compare to other passenger-oriented modes. Webdigger can probably find some details, but here are a few tidbits:

Compare to cars: similar to trucks, though less impact per vehicle (just, lots more vehicles). Except on toll roads, cars don't nearly cover the cost of building and maintaining roads for them even controlling somehow for the effect of trucks and buses. Improvements in fuel economy over the last 10 years or so (especially: alternative fuels that don't get highway-taxed, and generally reduced use of fuel per mile traveled) have only made it worse. The Highway Trust Fund is broke because it's still funded by taxes at a rate set when the light duty fleet average fuel economy was more like 20 mph instead of the near-30 it is now.

Compare to buses: similar to trucks in almost every way. They're heavy duty vehicles, and single-rear-axle buses can have some of the heaviest axle loadings allowed on a road without a permit. As with trucks and cars, their fuel economy has improved over the last 10 years or so, reducing their contribution per mile to the road funds at the same time they need more road construction for congestion relief to allow them to compete better with Amtrak.

Compare to airlines: the airlines themselves sometimes make money, even after paying airport fees (although major airports are publicly owned and operated, they are usually "enterprise" operations that have to cover their costs from direct income) and various taxes (which cover most but not all of the ATC cost). Competition at times has been ruthless, but currently is much subdued because of mergers and, probably, undisclosed agreements. Airport "slots" are also limited in places with high demand. Of course, there's also the program to subsidize service to small airports that don't make sense otherwise.

Compare to general aviation: no comparison - GA is massively subsidized. Few GA airports make money or even cover operating cost unless they have a LOT of traffic, and the airlines pay for the ATC system that GA uses. So yes, it's nice to be able to jump in your Cub (or Cessna, or Gulfstream) and fly off someplace, but don't even dream of claiming that you're paying your own way.

Compare to urban transit (rail or bus): this is probably the most valid comparison. Both Amtrak and transit are primarily social service operations that support other things - such as the ability of low-wage workers to get to work or shopping without cars (which many have to do). The current economy is based on low-wage workers, and getting more so (middle-income is vanishing), and the cost of having a car and using it must be balanced against rent. Transit is generally required to cover at least 20-25% of operating cost from the farebox to qualify for federal operating subsidies and, often, capital grants as well (I don't think Webdigger will be able to find ANY example of public transit, anywhere in the world, covering more than 50-60% of operating from the farebox with all capital coming from grants or other non-fare sources; that includes BART and commuter trains).

Amtrak itself: the long-distance trains are a social service operation. With extreme attention to cost control, Amtrak seems to be able to run most long-distance and regional trains at 40-60% operating cost from the farebox - which is much better than all but the best transit operations (BART seems to run around 50%). Throw the NEC in and farebox recovery for operations approaches 100% (plus a bit or minus 10-15% in any given year). That's better than nearly any non-HSR passenger train operation in the world, and can probably be improved further with a few tweaks (and freight railroads that actually help rather than hinder the trains). But it still needs Other People's Money for capital projects like replacing ancient bridges, locomotives, and cars.

HSR? Current lines are all over the place regarding cost recovery. Some TGV lines have (after more than 30 years) actually made enough money to cover not only operations, but also ongoing capital and original cost. Probably, some of the Japanese lines likewise. Italy has privatized the trains, so we'll see how well that works - but the govt still owns the tracks. China frankly doesn't care - they need the trains for economic support and prestige. HSR in general has at least a good shot at covering operating cost because it can operate like a transit line (many trains) but over longer distances (so they can charge decent fares). The high speeds certainly require more maintenance of both trains and tracks than conventional rail, but also produce higher utilization of equipment and staff. So I would not be surprised at all if a CAHSR line makes money (once the mountain lines are done so through service can be established) on operations - though it's probably 50-50 whether or not the original capital or ongoing capital maintenance (train replacements...) can be covered.