I think Clinton would have a rally around the flag effect, not as strong as Bush's was after 9/11 OTL, but strong enough to get his hand picked successor Gore elected. We'd probably invade Afghanistan in October of 2000, get Bin Laden sometime in early 2001 and the war would rap up sometime in 2002 or early 2003. Unfortunately we'd still have something along the lines of the Patriot Act, I don't think we'd get a Department of Homeland Security in a Gore administration as I doubt a GOP controlled house (I think they'd still keep it, the Democrats however will take the senate in 2000 TTL though) will allow another govt. department to form under Gore.
We launch a few airstrikes on Iraq, but we don't go to war, President Gore is defeated in 2004 by Senator John McCain, who is defeated in 2008 by Senator and former First Lady Hillary Clinton.