“At that point the president said, ‘That’s good to know,’” Mr. Hooper said.
But Mr. Byrne banked over $2 million after the first fund-raising quarter of the year, impressing many Republicans, and a handful of potential primary opponents indicated they would not enter the race.
Senator Todd Young of Indiana, who heads the National Republican Senatorial Campaign Committee, telephoned Mr. Trump earlier this month to make the case that Mr. Moore can’t win and express his hope that the party can be unified in its opposition to him, according to two Republican officials familiar with the conversation.
Mr. Young was acting at the behest of the Senate majority leader, Mitch McConnell, who has made no secret of his contempt for Mr. Moore and his determination to derail his candidacy. In 2017, a “super PAC” aligned with Mr. McConnell spent $6.9 million in the Alabama primary opposing Mr. Moore and in support of a more establishment candidate, former Senator Luther Strange.
Mr. McConnell and other leading Republicans privy to internal polling data from Alabama believe Mr. Moore is politically weakened but, recognizing that he still enjoys a loyal following of evangelicals, not to be ignored.
Senior Republican officials say they are all but resigned to another Moore candidacy, saying his income depends on his remaining in the political spotlight.
“There’s a lot about Roy Moore that still needs to be examined, especially on the financial element, it’s a tangled web,” said Kevin McLaughlin, the top aide at the Republican Senate committee, calling himself “A.B.R.M — Anyone but Roy Moore.”
If Mr. Moore does find his way to the nomination, it would complicate Senate Republican efforts to retain their three-seat majority. Assuming any mainstream Republican would win the deep-red state in a presidential year, party leaders have been banking on capturing Mr. Jones’s seat, and forcing Democrats to find four seats, rather than three, to reclaim the chamber.