Graham noted Republicans are in a lose-lose position when it comes to Moore. Last week, Trump made a similar statement about the race, not endorsing Moore but telling reporters, "We don't need a liberal person in there, a Democrat".
"It is pretty clear to me that the best thing that Roy Moore could do for the country is move on", Scott, R-North Charleston, said on ABC's "This Week".
He also pointed out that Moore "totally denies" the accusations against him and that the media "has to listen to him also".
In another tweet, he lamented the defeat of Senator Luther Strange, who Trump endorsed in the September primary vote against Moore. On Sunday the commander in chief doubled down on his support for Alabama Senate candidate Roy Moore by disparaging his opponent, Doug Jones, as "the last thing we need in Alabama".
Most of the women who have accused him of sexual misconduct said it occurred when they were teenagers and Moore was in his 30s.
Republican leaders briefly explored the possibility of seeking a write-in candidate but have determined those efforts would only increase Jones' chances by splitting the GOP vote in the Republican state. His campaign held an afternoon news conference to vigorously question the account of Beverly Nelson, who said Moore assaulted her when she was a 16-year-old waitress.
Just Tuesday, longtime Michigan Rep. John Conyers acknowledged that his office settled a sexual harassment complaint involving a former staffer, though he "vehemently" denied allegations in the complaint.
"If he wins, you get the baggage of him winning and it becomes a story every day about whether or not you believe the women or Roy Moore", Graham said.
"It's going to be a distraction for us and for our agenda", he said.
McConnell reportedly has pleaded with Trump to stay out of the Alabama race, lest Moore's election sully the party's name ahead of next year's midterm elections.
So, is it simpler to believe that Moore's accusers are paid political puppets, mere pawns in a complex political conspiracy, or that, as a grown man, Roy Moore once molested a child and often preyed on teenage girls? "He's definitely trying to throw a lifeline to Roy Moore". The special election is scheduled for 12 December.
"The president can speak for himself, as far as I'm concerned, the president can use his influence and do what he can to get Moore to step aside", Mr Thune said.