Ezra Klein has an excellent reported summary of the next steps in the Senate for health care. I'll build on his reporting here and talk about the procedural hurdles awaiting the bill on the Senate floor. This gets a bit technical, but if you want to know how the process might unfold here's a rough idea.
First, negotiations facilitated by Majority Leader Reid to produce a bill for the floor. Ezra has the key players as Baucus, for the moderates, and Dodd, for the liberals; the goal, apparently, is to take the Finance Committee product and add one of the versions of the public plan compromise (see here and here), plus some affordability things. The trick will be finding revenues to pay for those things, especially since liberals (labor, actually) aren't pleased with a major Finance Committee revenue source.
Second, the bill goes to the floor. As Ezra says, it will be relatively hard to change on the floor, since amendments can be filibustered, so liberal amendments will be defeated by 40 Republicans and some moderate Dems, while conservative amendments will be defeated by 40+ liberal Dems. Still, opponents are going to try to undermine it; look for Republicans to try to force tough votes, germane or not (I'll predict a gun amendment, for starters). Remember that anyone can offer any amendment on any topic, relevant or not, although they cannot force a substantive vote on amendments (but they can force procedural votes). If Reid, Baucus, Dodd, and the rest have done their work well, they'll have enough Dems committed to make the votes needed to keep the bill from taking on any dangerous baggage, and they'll have 60+ votes for final cloture for the bill that comes to the floor.
Now, Democrats can stop non-germane amendments by moving to cloture on the bill, which can happen at any time, including immediately upon bringing the bill to the floor. Marginal Democrats, however, may not be willing to vote for cloture on the bill before knowing what the final legislation will look like. Still, it's worth noting that we might see a very quick cloture vote on the bill. Another possibility is a test cloture vote early on. Basically, anything that can be debated can be filibustered, and then cloture can be invoked on that specific debate. So far this year we've had cloture invoked on overall bills, on specific amendments, and on the "motion to proceed," which is just the parliamentary procedure for bringing the bill to the floor.
Most bills are debated using complex unanimous consent (UC) agreements, which cover things like which amendments will be offered, in what order, and how long things will be debated. UC agreements can include a time certain for a final vote, but of course in this case Republicans aren't going to agree to that (although I suppose it's possible that, following a test vote on cloture on the motion to proceed, the Republicans could prefer to work out a full UC agreement rather than face an immediate cloture vote on the bill). It's likely that the parties will instead reach agreement on a partial UC agreement that will set up procedures for the portions of floor consideration that everyone agrees to, after which a cloture vote will begin to cut off deliberations.
We could easily see another 500 or more amendments filed, but the odds are that most of those will be either dropped without being offered or accepted without being debated. Still, it looks like they're going to take quite some time on the bill, probably around the same couple of weeks that the Finance Committee took.
So, that's what's coming up, at least as far as I can see, and pending any innovative floor procedures. I don't expect a lot of fireworks on the floor, to tell the truth. Ezra is correct: the real negotiations are going on right now, behind closed doors. Reid won't take the bill to the floor unless and until he has 60 votes, and sees a clear path that includes commitments from Democratic Senators not to change anything that would jeopardize 60.
[Update: links fixed]