You're thinking in terms of the false dichotomy that you either bail out a business or it goes under completely. Corporations declare bankruptcy and are bought and reorganized by healthier, better run corporations if they have any assets. That's capitalism in action. The free market, which Republicans lie about believing in, is about letting the best businessmen succeed, not the best connected businessmen. Bush and Obama didn't bail out the automotive industry, they bailed out the executives and unions that caused their financial problems in the first place.
Trying to force state-supported institutions to succeed, despite their failures in management (and ruinous union contracts) is socialism, which Republicans complain about when the Democrats are doing it.