Republican voters in Tennessee “don’t consider him an evil liberal person,” said Victor H. Ashe, a Republican and former longtime mayor of Knoxville. He predicted a tight race and said Ms. Blackburn could not afford to lose a significant chunk of Republican voters to her Democratic opponent.
In a nominal show of support for Ms. Blackburn, Mr. Corker wrote on Twitter last week that he was sending a donation to her campaign and wished her well in the Senate race. But in a brief interview, he said he would not campaign against Mr. Bredesen, recounting their long history working together and describing him as a friend.
“He was a very good mayor, very good governor, very good businessperson,” Mr. Corker said, adding, “He would be successful at anything that he did and is someone I consider to be very thoughtful.”
But there is ample reason for skepticism about Mr. Bredesen’s chances: No Democrat has won a statewide race in Tennessee since his successful re-election bid in 2006, and the state has turned more Republican since then. He will have to avoid being portrayed as being in lock step with national Democratic figures like Barack Obama and Hillary Clinton, as well as the top Democrats in Congress, Senator Chuck Schumer of New York and Representative Nancy Pelosi of California.
Ms. Blackburn and her allies “know that Bredesen is popular; they know that the national brand of the Democratic Party is not,” said Kent Syler, who teaches at Middle Tennessee State and was a longtime aide to former Representative Bart Gordon, Democrat of Tennessee. “So they will work very hard to connect him to that national brand, and he will work very hard to avoid that.”
Mr. Bredesen, 74, jumped into the race after Mr. Corker, a two-term Republican, decided to retire. A wealthy former health care executive who served as mayor of Nashville before becoming governor, Mr. Bredesen said he concluded that he was probably the only Democrat who would have a reasonable shot at winning the seat. In a video announcing his candidacy, he reminded voters of the successes of his tenure, including reining in the soaring cost of TennCare, the state’s Medicaid program, which had been financially troubled.
His decision to run for the Senate was a coup for Democrats in Washington who have been mapping out how to flip control of the chamber in November’s elections, even as their caucus defends 26 seats, 10 in states won by Mr. Trump, while the Republicans must guard only nine. Once seen as far-fetched, winning a majority is at least mathematically possible, especially after a Democrat, Doug Jones, won a special election in Alabama in December.
Skepticism of a Democratic takeover of the Senate has come from an unlikely voice in Tennessee: Mr. Bredesen. To Republicans who suggest a vote for him is a vote to make Mr. Schumer the majority leader, he pushed back on the idea.
“I don’t think it’s possible, I’ll be honest with you,” he said, naming Florida, Missouri and North Dakota as states where Democratic incumbents could be in danger. “My expectation is that I will be in the minority in the Senate.”
Mr. Bredesen is walking a careful line when it comes to Mr. Trump, who defeated Mrs. Clinton by 26 percentage points in Tennessee. “Look, I’m not running against Donald Trump,” he says in a television commercial that is textbook Bredesen sobriety.
In the interview, he emphasized his attentiveness to rural voters who feel like elected leaders are not doing anything to help them, recalling his own upbringing in upstate New York and offering a pointed critique of today’s Democratic Party.
“My party, I think, has gotten way too far to the left and needs to learn how to win elections,” he said. “I think we Democrats have gotten too elitist. We’ve gotten too narrow. We’ve gotten too involved in litmus tests.”
He continued: “I’d like to belong to a church that’s bringing new members in, not routing out dissidents or heretics or something like that, and I’m afraid we’ve gotten too much in the latter.”
Still, there are clear policy differences between Mr. Bredesen and the president. Mr. Bredesen said Mr. Trump’s promised wall along the border with Mexico was “political theater, not anything practical.” He also criticized the Republican tax overhaul for providing “crumbs” to the middle class — echoing a description previously used by Ms. Pelosi that Republicans eagerly seized on.
“I think they did something which was clever politically, but I couldn’t have swallowed morally, which is I think they threw a few crumbs to the middle class to give these huge breaks to wealthier people and corporations and so on,” Mr. Bredesen said. “And I think I would have called that out as strongly as I possibly could have.”
Ms. Blackburn speaks proudly of the tax overhaul, and she has allowed little distance between her and Mr. Trump.
“What we need in the U.S. Senate is a senator who is going to stand with President Donald Trump,” she told the crowd at a county Republican Party dinner in Murfreesboro this month, where a handful of young supporters wore red T-shirts that said “Marsha Marsha Marsha” on the back.
First elected to Congress in 2002 after serving as a state senator, Ms. Blackburn, 65, is a frequent presence on cable news channels. She has been a leading opponent of abortion, overseeing a House panel that investigated Planned Parenthood and the sale of fetal tissue for medical research. She once debated climate change with the television personality Bill Nye.
In a video announcing her candidacy, she described herself as a “hard-core, card-carrying Tennessee conservative,” spoke of carrying a gun in her purse, declared she was “politically incorrect” and said, with a note of pride, that liberals call her a “wing nut.”
But Ms. Blackburn’s full-throated conservatism is distinctive compared with the relatively moderate tone of Republicans whom Tennessee voters have sent to the Senate in the past — a group that includes Howard H. Baker Jr., a former Senate majority leader who became known as “the great conciliator”; another majority leader, Bill Frist; Mr. Corker; and Tennessee’s senior senator, Lamar Alexander.
In a Vanderbilt University poll conducted last year, 76 percent of Tennessee voters said they preferred that their legislators worked with the other party, even if it meant compromising on some of their values.
Ms. Blackburn is sending a different message. “Real conservative leadership,” promises a palm card for her campaign. “No compromise, no apologies.”
Representative Steve Cohen, a Democrat from Memphis, questioned whether Tennessee voters would embrace a candidate in that mold over someone with a middle-of-the-road, business-friendly image.
“We’ve never had a politician on that level of anybody that’s been kind of mocked for their antediluvian ways,” he said.
Ms. Blackburn suggested that people in Tennessee needed to get accustomed to the idea of being represented in the Senate by a woman.
“This is one of the things that you’ll hear people talk about from time to time, because Tennessee’s never had a female senator,” she said. “So it is going to be a little bit different, if you will. An approach will be different.”
Then there is the unresolved question of just how much Ms. Blackburn will be able to exploit Mr. Bredesen’s party affiliation — even if Mr. Bredesen himself is not eager to dwell on it.
Voters may have fond memories of Mr. Bredesen as governor, but will they want to help expand the ranks of the Senate Democratic caucus? Mr. Schumer personally courted Mr. Bredesen to run.
“You can’t talk one way at home and go to D.C. and support Chuck Schumer and expect that to be what the people of this state want,” Ms. Blackburn told the crowd in Murfreesboro. “And let me tell you something: Chuck Schumer as majority leader would be an absolute disaster.”
Mr. Bredesen scoffed at the idea that he would fall in line with Mr. Schumer, noting that he has a history of breaking with his party, including over the Affordable Care Act, which he roundly criticized.
“I’ve got a pretty good reputation as somebody who does not toe the party line on everything, which I think will help get through that,” Mr. Bredesen said of his opponent’s line of attack. “I’ve certainly made no commitments to be supportive of Chuck Schumer or anything else.”