Actually the governor can only appoint an interim replacement in the case of death, resignation, or refusal to serve by the member, or also in the case of expulsion of the member from the Senate. This power is granted to all state governors by the US Constitution Ammendment 17.
I'm no scholar on the Congress, but I don't think there has ever been a situation where a Senator was replaced while one party held power by so close a margin. This is based on the research I've been able to do quickly. There is a long-standing precedent of Senators holding their seats while incapacitated. Unless Sen. Johnson dies, I would expect him to hold the seat.