Actually, it’s not clear that a Lieberman defection would flip the Senate. The Jeffords defection only caused a switch because of a deal that Trent Lott and Tom Daschle had made in advance; no such deal is in place now. Thus leadership positions may be retained by the “majority” party even if they lose their numerical majority, as happened during the 83rd Congress.
That might go a long way toward explaining why Lieberman hasn’t jumped ship yet.



