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).