It is feasible to bail out Greece. If the European Union did not bail out Greece, then the whole economy of Europe would be in grave danger. Greece is too big to fail, so if the EU does not act on this, the whole world could be in danger. It may not seem feasible, but it has to be.
Greece can be bailed out, but it will take a combination of austerity measures combined with economic help from other nations. Greeks have already protested against austerity measures and the rest of Europe debated how much Greece needed to save its economy. Unfortunately, when the global economy tanks everyone pays. Greece was the unfortunate country caught in the crossfire in Europe as its weak economy was exposed during the Great Recession.