We are not the people?

I was sitting in bed (blech - I feel sick) and the news was on, and I saw this:

Guiliani:  America is its best, when people don't rely on the government, but each other.

...

Wait - I thought that "We the people" are the government.  That statement makes no sense.  And then I see:

Romney:  I don't want socialized health care from the people who brought you Katrina.

Me:  Wait, so the Bush administration, who set up clearly incompetent people to be in FEMA and other institutions, screwed up Katrina.  So because of this, you're saying that government can't do anything right.  Isn't the answer to elect and hire people who are competent, and then - like countries like England and Canada and France - we can have government that does a good job at disaster recovery and national health care and the like?

Why is it that people like Romney and Guiliani point at the incompetence of their own party to emphasize why "government is a bad thing"? 

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