Tori Venable, state director for Americans for Prosperity Tennessee, greets Jeanie Brakebill, 63, a retired nurse at her home in Knoxville Sept. 25. (Jessica Tezak/For the Washington Post)

Jeanie Brakebill voted for President Trump. But when a conservative canvasser showed up at the 63-year-old’s door here recently, she confided that she had grown tired of Trump’s confrontational brand of politics and was leaning toward voting Democratic in the upcoming midterm election.

“I would vote for Bredesen, to help out Tennessee — even if it means giving Democrats the majority in the Senate,” said Brakebill, referring to Democratic Senate candidate Phil Bredesen.

The sentiments expressed by Brakebill and voters like her have raised fresh worries for Republicans in this deep red state, which overwhelmingly supported Trump in 2016 but where voters remain divided just weeks before a midterm election that could determine which party controls the Senate.

Rep. Marsha Blackburn (R) is locked in a tight race against Bredesen, a popular former governor running on a moderate platform and a deep well of goodwill from his eight years in office. Recent polls show Republican voters in Tennessee and nationally are becoming more galvanized amid a bruising confirmation battle over Trump’s Supreme Court pick, but GOP strategists have been frustrated that Blackburn has not established a comfortable lead in the race to replace retiring Sen. Bob Corker (R).

GOP groups are deploying their full arsenal. Americans for Prosperity, the political arm of the conservative Koch network, on Wednesday announced a $2 million television ad campaign attacking Bredesen, on top of the $2.5 million it already spent on the race. The Senate Leadership Fund, the main Senate GOP super PAC, which spent $2.5 million on ads in the state so far, said it plans to spend roughly $3 million through the fall.

And Blackburn’s backers are banking that although some voters are souring on the president, vocal support from Trump will boost turnout among the GOP base. Trump made his second visit to the state Monday in support of Blackburn, telling a packed rally that “a vote for Marsha is really a vote for me and everything that we stand for.”

The difficulty for Republicans stems in part from the unique politics of Tennessee, and the fact that Bredesen, who left office in 2011 but has remained a household name, kindles a nostalgia for less-divisive times. He is a pro-business politician more in the mold of Corker, a moderate Republican who has sparred with Trump, than is Blackburn, who is deeply conservative and one of the president’s most loyal backers.

“Tennessee has a reputation for being super Republican, super conservative, and it certainly is a red state, there’s no debate about that,” said John Geer, polling and political science expert and dean of the Vanderbilt University College of Arts and Science. “But I don’t think it’s quite as red as some people think.”

Rather than railing against Trump as other Democratic candidates have done nationally, Bredesen has praised some aspects of the president’s agenda, such as his efforts to strike down regulations on businesses.

Bredesen also has pledged to withhold support for Senate Minority Leader Charles E. Schumer (D-N.Y.), whose name in this state is synonymous with liberal combativeness. The disavowal comes although Bredesen has received help from a Schumer-aligned group, Majority Forward, which has spent $3.6 million on television ads in Tennessee, with $2.7 million in reserve.

Conservatives have sought to remind voters that the careful balancing act Bredesen is attempting is more difficult in polarized Washington — a fact laid bare by the upheaval over Supreme Court nominee Brett M. Kavanaugh.

Bredesen has refused to say whether he would vote for or against Kavanaugh — one of the biggest questions facing moderate Senate Democrats.

In an interview Wednesday, Bredesen demurred when asked his position on Kavanaugh. But he argued that, at age 74, he can be relied on to serve as an independent voice because he has no ambitions for higher office beyond the Senate. He said the fact that the race remains competitive is a sign that his centrist message is appealing to voters across the political spectrum.

“I’ve got to rally Democrats. I’ve got to persuade a bunch of independents . . . [and] business [minded] Republicans,” he said. “But I did it as governor, and I think quite successfully. The fact that this campaign is obviously very competitive right now is evidence to that.”

In Bredesen’s equivocation over Kavanaugh, Republicans see an opening to drive up support for Blackburn, who has said firmly that she would vote to confirm the federal judge. Blackburn declined an interview with The Washington Post.

“It’s not about Brett Kavanaugh, it’s about the raw power of the Democratic Party . . . the meanness the Democratic Party will go to, to put one of their own” on the Supreme Court, Brian Hornback, chair of the Center City GOP in Knoxville, said at a recent committee meeting at a local chain restaurant in Knoxville.

Still, this is not where Republicans had hoped to be — not in solid-red East Tennessee, and certainly not so close to Election Day. At a time when activists had hoped to be focusing more on voter turnout than on persuasion, they were contacting hundreds of voters every day in an area that has voted Republican since the Civil War.

The Supreme Court battle has helped move the needle toward Blackburn among Republican-leaning and independent voters who are tired of partisan bickering, said Tori Venable, the Tennessee state director for Americans for Prosperity, whose activists are working across the state to persuade voters. The group is not letting up, as the race remains competitive, she said.

Blackburn is touting her conservative bona fides and is attacking Bredesen’s past support for Hillary Clinton and other national Democrats. Her hardcore brand of conservatism — she says in her announcement video that she carries a gun in her purse — is fueling the Republican base, which believes Blackburn has fought for their values during her 16 years in the House.

“I get up every day and I go fight for five things: Faith, family, freedom, hope and opportunity,” Blackburn said in a debate with Bredesen last week. “Tonight, what you saw was one who’s going to be a fighter for those things and individual freedoms, and one that is going to support bigger government and big-government solutions.”

The Republican strategy against Bredesen was encapsulated in an attack ad unveiled Wednesday that seeks to link him to prominent Democratic lawmakers in Washington and spur voters to envision a Democratic-controlled Senate.

“If Phil Bredesen wins, Dianne Feinstein picks your judges, Bernie Sanders runs the budget and Chuck Schumer runs everything,” says the narrator of the commercial from the National Republican Senatorial Committee, as ominous music plays.

But tethering Bredesen to Washington Democrats has proved to be a challenging task. He has never served in Congress and has crafted a reputation at home that has been difficult for Republicans to pierce.

Bredesen’s affiliation with the Democratic Party is no doubt a dealbreaker for some GOP voters who are mindful that control of the Senate hangs in the balance — including some who think he was a decent governor.

“Bredesen was one of the best governors we ever had. Problem is, he’s a Democrat,” said David Singer, 85, a retired professor and Blackburn supporter, after eating breakfast at a cafe in Murfreesboro, about an hour’s drive south of Nashville. “I’m afraid of upsetting the balance between the Republicans’ and the Democrats’ hold on the Senate right now.”

But while Blackburn inspires the base, she is alienating some more-moderate Republicans who have grown weary of Trump’s brand of incendiary rhetoric and view her as an extension of the polarization in Washington.

Thomas Cigarran, the chairman of the Nashville Predators hockey team and a longtime GOP donor, said he and his Republican peers are supporting Bredesen because they view Blackburn as a “poster child” of an ideologue.

“Marsha is going to vote the party line. That’s it,” he said. “We have way too much of that already. There’s no indication in the 16 years that any change in her behavior would be forthcoming. She is who she is.”

Cigarran hosted a fundraiser at his Nashville home last week in support of Bredesen. About 40 of his 50 guests were Republicans who were similarly frustrated, he said.

Another challenge for Blackburn: the lukewarm reaction to her candidacy from Corker.

Earlier this year, Corker lavished praise on Bredesen — drawing concern from Senate Majority Leader Mitch McConnell (R-Ky.), who told Corker in a private conversation that he was not being helpful.

Asked Wednesday whether he had any plans to campaign for Blackburn, Corker said he had been to a rally and two fundraisers. He said that he will be out of the country next Monday but that his wife will attend an event for Blackburn that evening.

Anu Narayanswamy contributed to this report.