Sen. Lindsey Graham of South Carolina shared a close friendship with the late Sen. John McCain for more than 20 years. From the halls of the Senate to the campaign trail, to nearly 50 overseas trips to war zones, their bond was a rarity in a rancorous Congress.

Graham said he found President Trump's response to the Arizona Republican's death "disturbing," with Mr. Trump ignoring reporters' questions about his passing in addition to the White House flag lapse.

Graham also told "CBS This Morning" co-host John Dickerson that while he's open to working with the president and will do "everything" he can to help the commander-in-chief, Mr. Trump's past comments about the military hero bother him "greatly."

"It pisses me off to no end, and I let the president know it," Graham said.

Mr. Trump has said McCain, who was a prisoner of war in Vietnam for more than five years, is "not a war hero," adding, "He's a war hero 'cause he was captured. I like people that weren't captured, OK?"

Read the transcript of Graham's interview below.

Sen. Lindsey Graham of South Carolina with "CBS This Morning" co-host John Dickerson CBS News

JOHN DICKERSON: If you, back in the Senate, could pass some legislation, not to honor him or name this building, what would you try and get passed?

LINDSEY GRAHAM: Immigration. … I want to get that done 'cause it meant a lot to John to fix a broken immigration system. …The president can do this. He is a deal maker. But the people around him, not so much.



DICKERSON: People would say the real disconnect between your effort to try to work with the president and your friendship with John McCain is, people say, all the praise that's being heaped on John McCain does not apply to the president.



GRAHAM: I am going to do everything I can to help President Trump, and when he's wrong, I will say so. … It bothers me greatly when the president says things about John McCain. It pisses me off to no end, and I let the president know it.

GRAHAM: The way he's handled the passing of John is just, was disturbing. We finally got it right. … I am not going to give up on the idea of working with this president. The best way I can honor John McCain is help my country.



DICKERSON: Did you call the president and tell him to bring the flag back down to half staff?



GRAHAM: No, but I called some people around him.



DICKERSON: What could the president learn from John McCain?



GRAHAM: What I would tell the president, you've got a lot of people you think are treating you unfairly. Fight back. But you're going to have to be a big man in a big office. John McCain was a big man, worthy of a big country. Mr. President, you need to be the big man that the presidency requires.



DICKERSON: Some people worry that getting rid of [White House counsel Don] McGahn means fewer people around him reminding him of the constraints of the presidency. Reminding him to be a big man, which you suggested.

GRAHAM: Well, as long as I'm around, I'll remind him of how this game plays. I've been involved in the impeachment of [President Bill] Clinton. I understand the process pretty well. Here – here's what I'll tell the president. There is no scenario where you can end this investigation, the Mueller investigation, through some political intrigue, and survive. That's the end of you. The only person in America that can clear Donald Trump is [special counsel Robert] Mueller.

DICKERSON: Do you think he'd fire Attorney General [Jeff] Sessions today if he could?

GRAHAM: I think he wants an attorney general that he has a better working relationship with. And to those in my business who say, "You're stuck with Jeff Sessions" – I like Jeff Sessions. But, I mean, do you have – how smart do you have to be to understand this – this is not working?



DICKERSON: Let me ask you about the Mueller investigation. You said that at the end of the day, if there is collusion between the Trump campaign and the Russians, that'll be it for me. Anything else will be just noise.

GRAHAM: Yeah.



DICKERSON: But you've said you have faith in Mueller.



GRAHAM: I do.



DICKERSON: So if Mueller finds something else, and it's not collusion –



GRAHAM: But then he'll act on it. … I say this as a joke, but it's kind of a half of a joke. To collude, you gotta sit down, come up with a plan, and stick with it. Trump's not good at that.



DICKERSON: But Lindsey Graham recognizes that an investigation may start here, and ultimately be cause for –



GRAHAM: Oh, 100 percent.



DICKERSON: So that could be possible in that case, too.

GRAHAM: Well, we'll – we'll see what he finds, absolutely.