A passenger train that runs 2-3 times a day (each direction) or less is an accommodation service for those who can't or won't use an alternative (usually driving). It can't make money or even break even, assuming affordable fares for those who are forced to (for lack of access to a car) or choose to ride it given its deficiencies and inconvenience. This describes the vast majority of Amtrak long-distance and even regional (with a few exceptions) services. Such service are important for social reasons, but must be subsidized.

A passenger train that runs 3-6 times a day up to maybe 12-16 times (each direction) is a convenient service that people will use, if it's reliable and has travel times even remotely comparable to driving. Many if not most such trains clear much of their direct operating expense from the farebox, and may even make a small "profit" on that basis. This describes some of the state-funded regional services (such as in California); not sure if Amtrak has anything like this outside of the NEC but a few of the Chicago-based corridor service might qualify, as might the Cascades. Public subsidy is still necessary to keep the fares somewhat "affordable" (i.e. competitive at least for business and individual travel), but there's a little slack in the fare-setting because the service is convenient. This is about as much as you can do on a line that also runs freight trains, and high end service even then is hard to interleave with more than a few freights during passenger operating hours.

A corridor that has more than 12-16 trains a day (counting all services) each way is either a transit line (like BART) or the Northeast Corridor, at least in the U.S. For practical purposes, it's a separate passenger line with little or no freight traffic. Speeds have to be fairly high for productivity - the trains have to stay out of each others' way. Assuming adequate cost control and enough demand that the trains run mostly full, that kind of frequency allows the train to be the preferred non-driving alternative in the corridor, and it will almost certainly make money at least on an operating basis. Some European HSR lines with this level of service actually do cover amortized (over a long period - 30-50 years) capital costs.

All the planning dreams for HSR assume it will be the last of those 3. If it is, the main reason for government involvement is to get it built, not to operate it, because amortization of the capital cost involved will take far too long for private interests to be involved. CAHSR will probably NOT be operated by Amtrak, as the current state-supported regional services are. Given that rail transit ridership projections tend to undershoot initial ridership but overshoot or be about right for long-term average, what's the betting line (LV style) on CAHSR being able to do it?