Luther Strange, Williams said, the conventional political wisdom was that if "even if he fell short", a close loss could set up a rebound for another statewide race. "He is the candidate".
A White House official clarified to The Times that Trump believes Moore should exit the race if the allegations are true.
At least nine women have accused Moore of making sexual or romantic advances toward them as teenagers. One of the women was just 14 at the time. The legal age of consent in Alabama is 16.
But Trump - himself the object of allegations of sexual misconduct by several women during his presidential campaign - on Sunday shrugged off such appeals.
Mr Moore has said he has "not been guilty of sexual misconduct with anyone".
Though several newspapers in Alabama published harsh denouncements of Moore last week, much of the state's Republican leadership has stood by the controversial candidate. But they were unsuccessful. But rather than condemn child molestation, Trump instead hit Moore's rival, Doug Jones, in a tweet Sunday morning.
Barkley, who made the remarks to reporters before the Alabama-Auburn football game, added that the backing from Bannon should have "disqualified Roy Moore way before this women stuff came up".
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"The last thing we need in Alabama and the U.S. Senate is a Schumer/Pelosi puppet who is WEAK on Crime, WEAK on the Border, Bad for our Military and our great Vets, Bad for our 2nd Amendment, AND WANTS TO RAISES TAXES TO THE SKY", he wrote from Florida, referring to Democrats' congressional leaders Chuck Schumer and Nancy Pelosi.
Graham went on to say that he doesn't see what winning looks like for Moore.
The Senate race has taken on even greater outcome as the Senate gears up for consideration of a massive tax-cut plan in which Republicans can afford to lose just two of the 52 members of McConnell's caucus. "He is a distraction", Mr Thune told TV host Chris Wallace on Fox News Sunday.
The South Dakota legislator suggested that while "ultimately the decision is up to the people of Alabama", Mr Trump can use his power to get Mr Moore to pull out of the race.
Meanwhile on NBC's Meet the Press, fellow Republican Senator Rob Portman (R-Ohio), said that the best thing for the country would be if Moore dropped out.
Republican Sen. Lindsey Graham of SC, who has also called for Moore to step down, said Sunday on CNN's "State of the Union" that Trump is "definitely trying to throw a lifeline to Roy Moore".