There is real historical experience with http://en.wikipedia.org/wiki/Sortition -- and AFAIK Athens wasn't worse-governed than the U.S. over its period of democracy. (It's true the scale is different.) Thinking we could just swap it in for elections seems silly, yes, but it could serve as part of a package of real reform.
Athens also had a much different population than we do and not everyone was eligible to be chosen. And I don't think it would go over well today to limit the pool of candidates to exclude those who are nominally unqualified for statecraft.
One great way around this is to alternate rounds of sortition with rounds of election:
- You pick 1000 random people to serve as the House of Representatives.
- They elect 100 people from among themselves to serve as the Senate.
- You randomly divide them into 10 person committees.
If you have enough rounds, there are some great effects:
- The election means that only competent or representative people make it through to the next round.
- The sortition makes it so that no one individual or small group is likely to make it all the way to the top.