More info:
Special election to fill senate vacancy
12-11-5. Special election to fill senate vacancy. The special election to fill the vacancy of a senator shall be held at the same time as the next general election. The general election laws shall apply unless inconsistent with this chapter.
12-11-6. No special election if appointed senator's term expires at normal time. No special election, to fill a vacancy, may be held if the term of office of the appointed senator expires in the month of January immediately following the next general election that would occur after the vacancy.
Source: SL 1979, ch 99, § 3.
http://legis.state.sd.us/statutes/DisplayStatute.aspx?Type=Statute&Statute=12-11-6
http://legis.state.sd.us/statutes/DisplayStatute.aspx?Statute=12-11&Type=Statute
Source: SL 1979, ch 99, § 2
All of theme:
CHAPTER 12-11
SPECIAL CONGRESSIONAL ELECTIONS
http://legis.state.sd.us/statutes/DisplayStatute.aspx?Type=Statute&Statute=12-11-5
So basically if Johnson has to be replaced, his replacement will just finish out his term as it is up at the next general election in 2008 anyway.