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"Actually, this is not how it's done, and it's not acccurate. The thing is, all of us have access to the bills that are introduced in either chamber."
That's usually the case with bills that are not controversial. But as one who has searched for bills and amendments related to FISA, war reauthorizations, torture, etc., I can tell you that those are not posted in a timely manner at the web sites you listed. Often, the only information we get about what's coming is from some congressional aides who "leak" the information to the press, groups like the ACLU, and bloggers like Glenn.
Sometimes draft bills end up online shortly before a vote, but only because some people (again, the ACLU, Glenn) are able to get their hands on them. Trying to find out what's happening with many of these bills before it's too late - and sometimes it is - can be maddening.