Could it be that massive government debt indicates the failure of capitalism?

Now don't get me wrong, as I'm not beating any political drums here. I know that socialist governments also have massive debt. But in a capitalist country isn't the private sector supposed to be the major part of the economy? If a government is running up debt to prop up a failing private sector (ie businesses too big to fail, putting money into the system, borrowing to sustain the economy) then essentially the people own that debt and the state is basically overriding the capitalist economy?

Thanks everyone for the informative answers. What I'm saying is that in a socialist system the state owns everything so we would not be surprised by government meddling in the economy. But in a capitalist system we would expect the government to, well, govern, and let private enterprise sort itself out. The fact that capitalist governments see fit to take out massive loans seems to indicate that a purely capitalist system does not work economically without significant intervention. Yes?