All the major U.S. airlines, other than Southwest, are losing money, mainly because of high oil prices (Southwest is an exception because they cleverly hedged their oil purchases). The airlines have been cost cutting for years; I assume that they can’t run their services significantly more cheaply than they do today. Therefore, on routes which are not busy, they are going to start raising prices and cutting service.
This will probably not have a big effect on people flying between large and medium-sized cities. Those prices may go up a bit, but the routes are heavily travelled, so competition between the airlines will keep the prices from going too high. Small cities, though, are often destinations for only one or two airlines. They are likely to see prices go up significantly, and some will see flights reduced or eliminated entirely.
Many of the domestic airlines have a lot of debt and limited room to maneuver. Even if that gets fixed, this is still likely to be a long-term trend, unless somebody develops a cheap alternative to jet fuel.
Train service in the U.S. is very limited, in part because government spending is heavily biased in favor of the automobile. So people in those small cities are going to have to drive to get other places. And, of course, gasoline prices are going up.
It seems to me that the likely long-term effect will be an accelerating depopulation of the rural U.S. As it becomes harder to get places, fewer people will be willing to move to them. The existing population will age and diminish. Over time, people will be more concentrated in fewer and denser cities.
I don’t see this as a bad thing, myself. The U.S. population has been steadily moving from rural areas to cities for over a hundred years now.
It’s also quite possible that something else will happen. Zeppelins can travel about 80 MPH today, and perhaps that can be pushed up some. They don’t require nearly as much infrastructure as trains do, and perhaps even less than planes. They’re too slow to cross the country, except as tourism, but they might be feasible as local transport to large airports.