While the governor of South Dakota is a Republican and could tip the balance in the Senate to a 50-50 tie, don't forget that Senator Thomas of Wyoming, a Republican, is currently undergoing treatment for leukemia. If Thomas has to resign, the governor of Wyoming, a Democrat, would appoint his replacement and that would blow everything wide open.
Prayers for Senator Thomas as well as Senator Johnson.
Maybe by that time, Harry Reid will be implicated in the Abramoff scandal and will have to resign, and since the governor of Nevada is a Republican we can switch back again, again.
-PJ
Wrong - The Republican Party of Wyoming would nominate three individuals, and the governor would have to choose one of them.
Replacement statutes vary by state..