Who knows what happens. Sounds like its got some strong backers on this committee. Markup matters if its contentious and there are opponents on the committee, but if there isn't much to slow it down then the opponents might sit back and let it go as is to the floor and then bring out their opposition.
Date will not be settled. What happens is that once it passes committee it becomes eligible to go to the floor. The date of that is a highly political issue, depends on what the leaders of the Senate think of the bill and how it fits into their plans. Sometimes they try to sneak it in as sort of warm-up type business when a big issue is about to hit the floor, other times they try to get it in some set of themes, ie it could be a part of a couple of anti-terrorism bills. Sometimes the leaders don't really like it so they give it a tough spot or don't even let it get to the floor. Tomorrow really isn't much of an issue and probably will tell little about what kind of battle to expect.