Nope, it is those carriers that had difficulties with a changed business climate even before the crisis that struggle now. Those that adapted continue to grow and even make billions of profit a year. Yup, even with those fuel prices. The demand is still there and prices are competitive but not disastrous.
Even those two airlines are just cutting their growth back a bit, not reducing overall capacity. United Continental expect to keep the same capacity and American even expects a 2.8% rise in capacity, at least according to that cited article.