“If you think about just the data from the past cycle, he’s a few thousand votes from being a United States senator,” said Mayor Walt Maddox of Tuscaloosa, the Democratic nominee for governor last year.
Mr. Moore’s rivals in the primary include Representative Bradley Byrne, whose 2010 campaign for governor fizzled out in a bruising primary (though he did garner more support than Mr. Moore in that race), and Tommy Tuberville, the former head football coach at Auburn University. John H. Merrill, a Republican who was re-elected last year as the Alabama secretary of state, is expected to announce his decision about a Senate campaign as soon as this month.
For his part, Mr. Moore has been on and off the national stage for decades, mostly because of his support for the public display of the Ten Commandments — a stand that contributed to his first removal from the Alabama Supreme Court — and his opposition to same-sex marriage, which played a role in what was effectively his second ouster from the high court. He has also drawn attention and criticism for his views on Islam and Sept. 11, and his uncertain command of some policy issues.
That history, along with the sexual misconduct allegations that surfaced in 2017, gives Mr. Moore’s rivals openings that they could exploit. They are also seeking something that Mr. Moore is unlikely to win for now: a presidential endorsement.
The sway of Mr. Trump, who won 62 percent of the vote in Alabama in 2016, could be influential but perhaps not decisive. In 2017, Mr. Trump endorsed another Republican candidate, Luther Strange, before Mr. Strange lost to Mr. Moore in a primary runoff. Only after Mr. Moore’s victory did the White House and the broader Republican establishment embrace him with an enthusiasm that proved uneven.
But with Mr. Jones seen as vulnerable next year, Republicans’ pre-emptive response to Mr. Moore’s 2020 bid tilted toward the hostile. Mr. Trump, in two tweets on May 29, wrote that Republicans could not afford to lose another Alabama Senate race and predicted that another campaign by Mr. Moore would stall.
“Roy Moore cannot win, and the consequences will be devastating,” he wrote.
One of Mr. Trump’s sons, Donald Trump Jr., was even more unstinting in his criticism: “You’re literally the only candidate who could lose a GOP seat in pro-Trump, pro-USA ALABAMA.” He added, “It’s time to ride off into the sunset, Judge.”