Polling on the race is limited, but one early survey suggests Blackburn may have a lead over Rose. A Fabrizio Lee & Associates survey from January found that 71 percent of respondents would vote for Blackburn in the GOP primary, while 13 percent said they would support Rose. Sixteen percent were undecided.

A conservative Trump ally in the Senate, Ms. Blackburn will now try to become the first woman to serve as governor.