"If he wins, we get the baggage of him winning, and it becomes a story every day about whether or not you believe the women or Roy Moore, should he stay in the Senate, should he be expelled?" Graham said on CNN's "State of the Union." "If you lose, you give the Senate seat to a Democrat at a time where we need all the votes we can get.
"The moral of the story is don't nominate someone like Roy Moore who can actually lose the seat any other Republican could win," the South Carolina Republican told anchor Dana Bash. "And what I would tell President Trump: if you think winning with Roy Moore is going to be easy for the Republican Party, you're mistaken."
Trump, who has all but endorsed Moore in the special election to fill the seat vacated by Attorney General Jeff Sessions, slammed Moore's Democratic opponent, Doug Jones, in a tweet early Sunday morning.
"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. Jones would be a disaster!" Trump tweeted.
Many Republicans, including Senate Majority Leader Mitch McConnell and House Speaker Paul Ryan, have disavowed Moore, pulling their support for his candidacy after several women accused Moore of pursing sexual relationships with them when they were in their teens and he was in his 30s.
David Urban, a former Trump campaign strategist, broke with the President on "State of the Union," saying, "I think the only thing worse than Doug Jones is Roy Moore.
"I think Roy Moore will be an anchor on the Republican brand," Urban said. "I think it will be a disaster for the midterms and the party will continue to try to move and separate itself. I think that the governor should have just postponed the election, it's well within in her purview to do so and could have solved it very easily."
One woman alleges Moore touched her inappropriately when she was 14. Another woman has accused Moore of sexually assaulting her when she was 16. The legal age of consent in Alabama is 16.
Moore has repeatedly denied the allegations, which Trump has emphasized when asked about the former Alabama chief justice's candidacy.
"He denies it. Look, he denies it," Trump said last week. "If you look at all the things that have happened over the last 48 hours. He totally denies it. He says it didn't happen. And you know, you have to listen to him also."
Moore wasn't the President's first choice for the nomination. Trump backed Luther Strange, who was appointed to finish out Sessions' term by then-Gov. Robert Bentley, in the primary, moving to support Moore only after Strange lost. Trump reminded his followers of that fact in a tweet Sunday morning.
"I endorsed Luther Strange in the Alabama Primary," Trump wrote. "He shot way up in the polls but it wasn't enough. Can't let Schumer/Pelosi win this race. Liberal Jones would be BAD!"
Trump's tweets on Sunday aren't his first swipe at Jones. Last week, he told reporters on the White House lawn, "We don't need a liberal person in there, a Democrat, Jones. I've looked at his record. It's terrible on crime. It's terrible on the border. It's terrible on military. I can tell you for a fact we do not need somebody who's going to be bad on crime, bad on borders, bad with the military, bad for the Second Amendment."