I think it might be helpful to look at this in two parts - the national/LD trains, and the state-supported trains.
On the national/LD front, the Sunset Limited is often singled-out by critics. However, that doesn't necessarily mean that it would be the first to be cut if Amtrak's funding situation causes tough choices regarding LD trains to be made. The Southwest Chief was threatened with a reroute or potentially cancellation because of poor track conditions in CO-KS-NM, but the situation seems to be improving there, with some federal grants to improve tracks. Really it comes down to how dire a situation Amtrak finds itself in. And how you think federal elections (president and congress) will change things a year-ish from now.
On the state-supported front, most corridors see multiple-daily service, so any funding cut would probably result in a reduction in frequencies before service on a corridor would be discontinued altogether. But, the Heartland Flyer is an exception, being the only train on its route, and there has been some speculation that OK/TX will not pay the increased charges in the coming years. The budget situation in IL is a mess right now, with the Governor and Legislature in a stalemate, so there could certainly be some problems there depending how it is resolved. It took quite some time for PA to agree to fund the Pennsylvanian, but that seems to have largely been resolved.
Of course, the situation in a state could change significantly with gubernatorial and legislative elections. We've seen that in an anti-rail way in OH and WI a number of years ago. It's possible that it could swing back in a pro-rail way in those states. Or that things could change for the worse in some other state.
