Senator Susan Collins, Republican of Maine, also expressed apprehension.

“Obviously some of his past writings are of concern,” she said. “Certainly, it appears that he has a lot of personal financial issues as well as troubling writings about women and our role in society, in sports — and also how he views the Federal Reserve.”

Senator Richard C. Shelby, Republican of Alabama and an influential former chairman of the Banking Committee, fretted on Tuesday in a closed-door Republican lunch that the issues bedeviling Mr. Moore could produce a volatile confirmation hearing.

“I hadn’t said I would vote for him or not vote for him,” Mr. Shelby said in a brief interview afterward. “But I raised these because these are troublesome issues that aren’t going to go away.”

Several White House officials privately acknowledged on Tuesday that Mr. Moore would most likely not be nominated — just over a week after Herman Cain, Mr. Trump’s other top pick for the board’s second open seat, withdrew from consideration after accusations of sexual harassment that had stopped his 2012 presidential campaign resurfaced.

But Larry Kudlow, the main benefactor behind Mr. Moore, told Mr. Trump as recently as Monday that Mr. Moore’s prospects were actually growing stronger.

Speaking on Sunday on ABC’s “This Week,” Mr. Moore expressed confidence that Republican senators would continue to back him despite the controversies. “I know most of the Republican senators,” he said. “I think they respect my economic expertise and my record.”