Unfortunately, the key challenge with the problem isn't architecting a DVCS-like service for legal documents (for an MVP, you could easily get by simply designing a novel frontend to git), it's an adoption problem. The current system is flawed, yes, but merely offering a superior product for less money isn't enough to make a dent in the bureaucratic nightmare of modern-day Washington.
I'm reminded of an article I saw here on HN a few months back: http://www.informationdiet.com/blog/read/dear-internet-its-n...
The question is how up-to-date the bill texts are. I doubt it can tracks in real time with changes/amendments voted on, etc. but then again any system bolted on the process as opposed to being fundamentally integrated into the process wouldn't be.
Your pessimism is unwarranted. There is already one user on GitHub that scrapes the US Code and mirrors it. He even tags the changes so you can diff them quite easily.
Here's an example of a service built on Ontario laws (disclosure: I made it): www.ontariomonitor.ca. It emails people when a bill passes a committee or when new laws are introduced (+ lots of other stuff).