If the senate makes changes/marks it up, and approves the Bill, as amended....it then goes BACK to the House, for approval (or further mark up). If the House accepts the changes made by the Senate, then it goes to the President for signature.
However, if the House makes changes to the Senate version---that's the part I'm not positive about, but I think it needs to go back to the Senate, yet again for approval, before it can go on to the President for signature. (It's been years since I've taken political science, but I think this is the very general workings of a bill (begun in the House; if begun in the Senate, the workings are the same, it just starts with SB instead of HB, of course).
In this particular bill, I don't know the exact status.....I'm sure another FReeper is more up to date on this.