“I don’t think the Lord Jesus could win as a Democrat in Alabama,” said Brad Chism, who runs a Democratic communications firm in Mississippi that has conducted surveys of female voters in Alabama in recent weeks. “They’re just waiting for the Republican Party to tell them how they’re going to fix this.”

Mr. Moore was never widely popular in Alabama, even among Republicans; his zealous fan base has been just enough in some past elections, and in others — his two poor showings in Republican primaries for governor — it has been far short of enough. The aversion to Mr. Moore has only grown more pronounced with the outbreak of sexual misconduct allegations, including one that he molested a 14-year-old girl — allegations that Mr. Moore denies.

But distaste for Mr. Moore, while it may lead people to write in other names or just stay home, is for many still not a good enough reason to vote for a Democrat. And here in Alabama, one of the most inflexibly partisan states in the country, where genuine swing voters are few and politics is approached with the same kind of unshakable team loyalty as college football, this is the central problem with Mr. Jones. He has been trailing in recent polls after a spasm of optimism that he could pull off a stunning upset in a state where Democrats have not won a major statewide race since 2006.

Alabama Republicans who are looking for an alternative to Mr. Moore are turned off by the Democrats over a constellation of issues — Supreme Court nominations, the scope of federal regulation, the fact that a Democrat would probably stymie President Trump’s agenda and the general sense that the national Democratic brand is in conflict with white Southern culture. But the obstacle that voters most commonly bring up, from the college town of Tuscaloosa to suburban Birmingham to Mr. Moore’s home county in northeast Alabama, is Mr. Jones’s stance on abortion.

“The biggest thing for me is that he’s pro-choice,” said Susan Moore, a retired respiratory therapist who said she had been unhappy with Mr. Moore (who is no relation) for years, frustrated by his flouting of the law while he was a judge. She said she admired Mr. Jones’s prosecution of the Ku Klux Klan members who helped plan the 1963 bombing of the 16th Street Baptist Church in Birmingham. But as for Mr. Jones in the Senate, she said, “I think he’s much too liberal for our state.”