Answer: Still unclear. Everyone on the Hill is referring such questions to the Majority Leader's office, and the Majority Leader's office isn't saying much. The Democrats (including Harry Reid himself) are wrapping up their weekly caucus lunch and Reid has scheduled a press conference for 2:45. We'll keep our eye on it.
There are at least two important questions that still need to be answered. First, what will Specter's committee assignments be now that he's a Democrat. And second, who will replace him on his current committees now that he's switching over. He was, of course, ranking member on the Senate Judiciary Committee, and, for good measure, ranking member on subcommittees in the Environment and Public Works Committee and the Appropriations Committee. Those positions will now have to be handed down to other Republicas.
More on all that later. But for now, keep in mind that the next most senior minority member of the Senate Judiciary Committee is Sen. Orrin Hatch (R-UT). He used to chair that committee, and there may be term limit rules that prevent him from taking Specter's place. Behind Hatch are Iowa's Chuck Grassley (ranking member on Senate Finance) and Arizona's Jon Kyl (the minority whip). If they don't swap out those coveted positions for Specter's slot on Judiciary, next in line would be...Sen. Jeff Sessions (R-AL).