Are the recent government bailouts to the banking industry proof that minimal government is no longer realistic?

First: I don’t know much about economics. This is not an opinion piece; I am genuinely looking for other people’s opinions, so please comment if you have an opinion on it.

I’m just watching The Love of Money and it was saying how Paulson and Bernanke said to the US government that if the banks didn’t receive a promise of a bailout then the entire banking system would collapse within 48hrs.

If we assume that this was true and the bailout was required, then does it suggest that the concept of a minimalist, libertarian-style government is no longer feasible? It’s my understanding that under such a tiny government there would be hardly any taxes, so how would it ever be able to nationalise so many financial institutions? Even putting aside that nationalising things would be anathema to such a government in the first place, it wouldn’t even be possible.

Or would proponents of such a style of government argue that this crisis would never have happened in the first place without government meddling?

I guess I am asking if lightweight government is incompatible with this global economy that we seem to have?