Here's a partial transcript to give the flavor of the thing, Trump's constant interruptions and his inability to articulate why he picked Pence (beyond the tactical consideration I mentioned):
Lesley Stahl: I have to move on or we're never gonna find out why he chose you. Why did you pick him? You had other candidates--
Donald Trump: OK, I did. I had a lot of people that wanted it; a lot more people than anybody--
Lesley Stahl: That came to you and begged you for it?
Donald Trump: That called me and came to me and wanted it badly. And you know, the press didn't report that. The press said, "Well, maybe he's having hard time picking--"
Lesley Stahl: Well, what about the governor? Did he want it like that?
Donald Trump: I actually brought it up to him.
Lesley Stahl: OK.
Donald Trump: I got to know him during the-- when I was in Indiana during the primaries, and I did very well in Indiana, like I did just about everywhere else in all fairness. But-- I got to know him very well and I gained great respect for him. And I looked at the numbers, meaning the financials, which we would say in business. But I looked at the numbers. Unemployment? What a great job he did. Jobs? What a great job he did. Triple-A rating on his bonds.
Lesley Stahl: --but you went to him and said--
Donald Trump: I did--
Lesley Stahl: Would you want to be considered--
Donald Trump: I broached it.
Lesley Stahl: He didn't -- And then he said, "I-- I really want it." So why did you pick him?
Donald Trump: I would say that he thought about it a little bit. And about two seconds later, he called me, with his incredible wife, and said--
Lesley Stahl: That I'd like to be-- but what--
Donald Trump: Like many others.
Lesley Stahl: How does he help you? How does he help you win in terms of groups of people? And what is your weakness that he compensates for and so forth--
Donald Trump: Well, I went for the quality individual rather than I'm gonna win a state, because I'm doing very well in Indiana, and I guess I'm a lot up. And I think I'm gonna win Indiana. I have a great relationship and Bobby Knight helped me so much with Indiana. Indiana's a great place; great state.
Lesley Stahl: Why didn't you pick him? No, I'm joking -- moving on.
Donald Trump: He would've been very good. But he's a terrific guy. But-- but I really like him as an individual.
Lesley Stahl: So you must've considered, obviously, by the reaction to your choice, a lot of the conservatives are very happy.
Donald Trump: Very happy.
Lesley Stahl: Was that part of the--
Donald Trump: Yes, it was party unity. I'm an outsider. I am a person that used to be establishment when I'd give them hundreds of thousands of dollars. But when I decided to run, I became very anti-establishment because I understand the system--
Lesley Stahl: Is he establishment?
Donald Trump: --than anybody else. He's very establishment, in many ways, and that's not a bad thing. But I will tell you--
Lesley Stahl: That's kind of interesting --
Donald Trump: --I have seen more people that, frankly, did not like me so much, and now they're saying, "What a great pick." You see the kinda reaction. He has helped bring the party together. I understand. Look, I got more votes than anybody, but I also understand there's a faction--
Lesley Stahl: Is it already unified, do you think?
Donald Trump: I think it's very close to unified. And I will say--
Lesley Stahl: Just because of this pick?
Donald Trump: No. I think it's be-- I think it was much more unified than people thought. You saw that with the recent vote where we won in a landslide. You saw that with the big vote, the primary vote. I think it's far more unified than the press lets on. But having Governor Mike Pence has really-- people that I wasn't necessarily liking or getting along are loving this pick, because they have such respect for him.
Lesley Stahl: And that was--
Donald Trump: And the party unity is OK. You know, I think it's OK to say I picked somebody, because I-- as one of the things. But I really believe the main reason I picked him is the incredible job he's done. Just look at the economics of Indiana--
Lesley Stahl: Indiana--
Donald Trump: --and what's going on.
Lesley Stahl: But what about the chemistry between you two? You don't really know each other that well. You're -- at least I've read, a very low-key, very religious, you're a brash New Yorker--
Donald Trump: Religious.
Lesley Stahl: Religious?
Donald Trump: Religious--
Lesley Stahl: Are you?
Donald Trump: Yea, religious.
Lesley Stahl: --you wouldn't--
Donald Trump: Hey, I won the evangelicals. The evangelicals--
Lesley Stahl: That doesn't--
Mike Pence: You know, nobody thought--
Donald Trump: --well, I think it means a lot. I don't think they think I'm perfect, and they would get up and they would say, "You know, he's not perfect," but--
Lesley Stahl: They'd point to the --
Donald Trump: --they like me--
Lesley Stahl: --divorces--
Donald Trump: --but I won-- I won states with evangelicals that nobody thought I'd even come close to--
Lesley Stahl: Well, that's true--
Donald Trump:-and I won--
Lesley Stahl: --so you didn't (UNINTEL)--
Donald Trump: --with landslides--
Lesley Stahl: --need him for the evangelicals?
Donald Trump: I think it helps. But I don't think I needed him, no, because--I won with evangelicals.
Mike Pence: But I think we have more in common--
Lesley Stahl: Yeah, tell me--
Mike Pence: --than--
Lesley Stahl: --what you think you have in common.
Donald Trump: --what might be immediately obvious.
Lesley Stahl: Besides issues. Values and things like that.
Donald Trump: I think we will have very, very good chemistry. I feel that. And I can feel that pretty early on. I don't think you need to be with somebody for two years to find that out. My feeling is-
Lesley Stahl: Your gut feeling.
Donald Trump: I knew him during the primaries, during many trips to Indiana, I'd be with him. I think we have a great chemistry.
Lesley Stahl: I want to ask you though about something you've said about negative campaigning.
Donald Trump: Yeah.
Lesley Stahl: You said negative campaigning is wrong, and a campaign ought to demonstrate the basic decency of the candidate.
Mike Pence: Right.
Lesley Stahl: With that in mind, what do you think about your running mate's campaign and the tone and the negativity of it?
Mike Pence: I think this is a good man who's been talking about the issues the American people care about.
Lesley Stahl: But name-calling?
Mike Pence: In that--
Lesley Stahl: "Lyin' Ted?"
Mike Pence: --in the essay that I wrote a long time ago, I said campaigns oughta be about something more important than just one candidate's election. And-- and this campaign and Donald Trump's candidacy has been about the issues the American people care about.
Lesley Stahl: --but what about--
Donald Trump: Lesley, Lesley--
Lesley Stahl: --the negative side? He apologized for being a negative--
Donald Trump: We're different people. I understand that. I'll give you an example. Hillary Clinton is a liar. Hillary Clinton-- that was just proven--
Lesley Stahl: That's--
Donald Trump: --last week.
Lesley Stahl: --that's negative--
Donald Trump: Hillary Clinton--
Lesley Stahl: By the way --
Donald Trump: --you better believe it. Hillary Clinton is a crook.
Lesley Stahl: That's negative--
Donald Trump: I call her "Crooked Hillary." She's crooked Hillary. He won't-- I-- I don't-- I didn't ask him to do it, but I don't think he should do it because it's different for him.
Lesley Stahl: But-- he--
Donald Trump: He's not that kind of a--
Lesley Stahl: He probably--
Donald Trump: --person. We're different people--
Lesley Stahl: --don't you think he--
Donald Trump: --to me she's--
Lesley Stahl: --thinks that's--
Donald Trump: --Crooked Hillary.
Lesley Stahl: --wrong?
Donald Trump: I don't think he should use that term. I've never said one way or the other. But to him, I don't think it would sound right, but he will say how dishonest she is by going over the facts.
Lesley Stahl: But would you go to him-- let's say you won, you're the vice president, your office is, I assume, down the hall, and you go in and you say, "You know, you shouldn't be saying-- name-calling." Would you do that? Would you go in and say, "You crossed the line, I think you should apologize?" Would you do something like that?
Mike Pence: Look, I--
Lesley Stahl: He's laughing.
Mike Pence: --it's probably-- it's-- it's probably--
Lesley Stahl: It's OK.
Mike Pence: --obvious to people that our styles are different. But I promise you, our vision is exactly the same.
Lesley Stahl: No, but would you--
Mike Pence: And let me be--
Lesley Stahl: --will--
Mike Pence: --clear--
Lesley Stahl: --will you answer that? Would you go in --
Mike Pence: Well the-- one of the things I found out about this man is he appreciates candor. And--
Lesley Stahl: So you would go in--
Mike Pence: --I-- I--
Donald Trump: I'd like him to if he thinks I was doing something wrong--
Lesley Stahl: Would you listen--
Donald Trump: --just say--
Lesley Stahl: --to him--
Mike Pence: Yeah.
Lesley Stahl: --if he said you--
Donald Trump: Absolutely--
Lesley Stahl: --crossed the line.
Donald Trump: --absolutely. I might not apologize. You know, you said apologize, but--
Lesley Stahl: I did say apologize.
Donald Trump: But I might not do that, but I would absolutely want him to come in-- if he thinks I'm doing something wrong, Mike, I would want him to come in and say, really, you're doing, you gotta-- and that's OK. I accept that from my consultants and my people and if Mike came in and told me, you know, "I think you should do this or that--
Lesley Stahl: Back off that.
Donald Trump: I would listen and very likely listen to him.
Lesley Stahl: Do you think John McCain is not a hero because he was captured?
Mike Pence: I have a great deal of respect for John McCain, and--
Lesley Stahl: Do you think he went too far?
Donald Trump: You could say yes. I-- that's OK.
Donald Trump: That one, you could say yes, I mean, you're not--it's fine - hey, look, I like John McCain. But we have to take care of our vets.
......
....Donald Trump: You know-- the Constitution -- there's nothing like it. But it doesn't necessarily give us the right to commit suicide, as a country, OK? And I'll tell you this. Call it whatever you want, change territories, but there are territories and terror states and terror nations that we're not gonna allow the people to come into our country. And we're gonna have a thing called "Extreme vetting." And if people wanna come in, there's gonna be extreme vetting. We're gonna have extreme vetting. They're gonna come in and we're gonna know where they came from and who they are.
Mike Pence: You just asked me--if I'm comfortable with that--
Mike Pence: --and I am. What-- what Donald--
Lesley Stahl: You're on the same--
Mike Pence: Which--
Lesley Stahl: --page on that?
Mike Pence: --clearly-- clearly this man is not a politician. He doesn't speak like a politician--
Lesley Stahl: He's done pretty well.
Mike Pence: --he-- he speaks from his--
Mike Pence: --heart--
Donald Trump: Is that a good thing? I think that's a good thing.
Mike Pence: --he speaks from his heart. And--
Lesley Stahl: Well, I--
Donald Trump: Well, I-- I speak from my heart and my brain. Just so we understand.
Mike Pence: Right.
Donald Trump: This is (points to head) maybe more important.