"You can put the Republicans in a very small car who are going to follow Rand Paul's advice when it comes to national security," Graham told CNN's John Berman and Kate Bolduan on "At This Hour." "He is my friend, he's a libertarian, but he's an outlier."
Graham expressed confidence that both Giuliani and Bolton could be confirmed as heads of the State Department despite early opposition from Paul and Democrats, who have seized on Giuliani's international consulting work and paid speaking engagements -- something Hillary Clinton was criticized for -- as potential conflicts of interest. He also dismissed Paul's complaint about the hawkish Bolton since his recess appointment during the Bush administration.
Graham also said he could support another potential candidate -- his state's governor, Nikki Haley -- though his backing was more lukewarm.
"I would say (Haley) did a good job as governor of South Carolina. She's talented, she's capable. I think she could do a good job in any assignment given. I don't know about her foreign policy. I haven't talked to her," he said, adding later, "At the end of the day, I would support her."
Graham opined on Texas Sen. Ted Cruz as a potential pick for the Supreme Court vacancy, an idea --perhaps jokingly -- floated by Graham himself, despite a long history of criticizing the Texas firebrand. He had remarked earlier this week the largely unpopular Cruz would easily win a confirmation from his Senate colleagues, insinuating they might be eager to be rid of him.
"Ted Cruz is a constitutional conservative, very, very smart, in the mold of Scalia," Graham said, referencing Justice Antonin Scalia, who passed away earlier this year.
"The people on (Trump's) list ... I could support them all. I just suggested that if you are looking for a Scalia-type figure, somebody to replace judge Scalia in their image judicially, Ted Cruz would fit that bill," he said.
And Graham also said that he approved of Trump's apparent moves to install his son-in-law, Jared Kushner, as an adviser, despite the controversy and charges of nepotism.
Graham said it would be "fine with me" if Kushner worked as a senior adviser.
"It shows they got a good relationship. I don't know how many father-in-law's would pick their son-in-law's to do anything."
While he enthusiastically supported some of Trump's potential administration appointees, Graham -- who serves on the Senate Armed Services Committee -- expressed a firm willingness to challenge the new president on policy. As one of the more moderate Republicans in a closely divided senate, Graham could be positioned to wield significant influence in close votes.
"I can tell you if I disagree with the president," Graham said. "I'm going to push back when I need to push back."
On the issue of Russian aggression, Graham sounded a more bellicose tone than Trump, who has urged friendlier relations.
"I have a different view of Russia. I don't think (Vladimir) Putin's our friend," he said.
And Graham also stressed that counterterrorism efforts shouldn't be used as an excuse to permit Syrian dictator Bashar al Assad's atrocities.
"I see Assad as the butcher of Damascus ... I don't see Assad as an ally or friend of the United States," he said.
Finally, Graham put some space between himself and Trump on immigration reform, saying he will "vote for any bill that secures our border," but that "I'm not going to vote for a bill that can't tell the difference between a grandmother who has been here illegally and a drug dealer. I just can't go there."