Republicans control significantly more state governorships than Democrats, both in 2001 and now. So -- and again, this is without my checking for state statutes governing appointments vs. special elections -- you have the potential to radically reshape the composition of the 2001 Senate after the "decapitation strike, which at the time was 51-49 Democratic (after Jeffords' defection).
Moreover, as I look closely at it, a significant chunk of the Democratic leadership comes from states that in 2001 had Republican governors, incluidng CT (John Rowland), FL (Jeb Bush), IL (George Ryan), MA (Jane Swift), MI (John Engler), NV (Kenny Guinn), NJ (Donald DiFrancesco), NY (George Pataki), RI (Lincoln Almond), and WI (Scott McCallum).
If they all can appoint new Senators, that's a potential net swing of 17 seats to the Republicans, and take a look at who the Democrats would lose: Ted Kennedy, John Kerry, Dick Durbin, Harry Reid, Hillary Rodham Clinton, Chuck Schumer, Carl Levin, Russ Feingold, Chris Dodd, Joe Lieberman, Bob Graham, Bill Nelson, Debbie Stabenow, Jack Reed, Herb Kohl, Bob Torricelli, and Jon Corzine. (!)
Obviously, the Republicans will lose some of their prominent Senators as well, but the Republican bench in 2001 draws heavily from a lot of Governors. So not only will you get a more militant, rally-around-the-flag administration and Congress, but you will probably wind up with a significantly more conservative Senate and an opposition party that can either go with candidates who are distinctly not ready for prime time (Dean, Obama) or retreads (Al Gore).