As Gloria Johnson, the Democratic candidate for Senate in Tennessee, has driven from diner to coffee shop to restaurant across the state, she has been met with a chorus of enthusiasm that a Democrat has shown up — and resignation that it most likely still won’t matter.

Her Republican opponent, Senator Marsha Blackburn, an uncompromising fiscal conservative and a loyal ally of former President Donald J. Trump, is widely expected to coast to re-election.

So Ms. Johnson, who gained unexpected prominence as one of the “Tennessee Three” gun control advocates, has instead shaped her long-shot bid around channeling frustration over Republican dominance into better turnout down the ballot.

“What I was thinking about was the importance of flipping the State House and the State Senate,” Ms. Johnson said, describing her decision to run. And that, she added, required “somebody at the top of the ticket who was really speaking to Tennessee voters about how things could be better.”

As in much of the South, Democrats in Tennessee are mired in the depths of the minority under both a Republican governor and a supermajority in the State Legislature. A Democrat has not won a statewide election since 2006, and Republicans have spent years pressing their advantage by using redistricting to ruthlessly carve up the few remaining splashes of blue voters into conservative districts.