The following is a script from "The Democratic Ticket," which aired on July 24, 2016. Scott Pelley is the correspondent. Henry Schuster and Ruth Streeter, producers.

Tonight, we have the first and only interview with the new Democratic ticket. Last Sunday on 60 Minutes, we heard from Donald Trump and Mike Pence. Now, on the eve of the Democratic convention we will hear from Hillary Clinton and her running mate Tim Kaine.

Hillary Clinton, right, and running mate Sen. Tim Kaine CBS News

She introduced Kaine yesterday at a rally in the critical battleground state of Florida. Kaine has been a city councilman and mayor in Richmond, Virginia, then Virginia's lieutenant governor, governor, and now U.S. senator. We asked the Democrats about fixing the economy, fighting terrorism and their shared vision of the future.

Scott Pelley: Why Tim Kaine?

Hillary Clinton: Well, as I have said throughout this whole process, the most important qualification is that the person I pick be ready to become president if something were to happen. I don't think there's any greater responsibility. So he's highly qualified. He's been a mayor, a governor, a senator. Secondly, he's a progressive who likes to get things done. That's how I describe myself. And I look at his record, his civil rights record, his education record, his taking on tough issues like gun safety, climate change. The whole picture is one that I find, you know, very appealing. And then finally, I want somebody who will be candid and will tell me, "Hey, I don't agree with this," or, "Could you think about it somewhat differently?" I don't think I have all the answers. I think that we'll be a good team. I believe we'll work well together. I believe that he will give me his best advice.

Scott Pelley: Senator, what did you tell her you were good at?

Tim Kaine: You know, I've been a city councilman and mayor. I've been a lieutenant governor and governor and now in the Senate serve on the Armed Services and Foreign Relations Committee. So I'm a utility player. I just want to do everything I can to make sure A) we win and that B) the presidency of Hillary Clinton is fantastic. And I think I can -- with my two cents, I think I can help that happen.

Hillary Clinton: I do, too. And, well, I just have to add that he plays a mean harmonica.

Scott Pelley: I heard that.

Hillary Clinton: Yeah, yeah.

Tim Kaine: Gotta have a fallback in my line of work.

Scott Pelley: Senator, you're gonna be vice president in a White House with two presidents.

Tim Kaine: I mean it's an embarrassment of riches.

Scott Pelley: What do you think of that notion?

Hillary Clinton: I think it's an all-hands-on-deck time. We're gonna have a cracker jack staff. And we're going to have, you know, great efforts with our congressional allies and others.

Scott Pelley: When we wrote that question, I expected you to come up out of your chair at me and tell me that there was only going to be one president.

Hillary Clinton: Well, no. Because I will be the president. But it does happen to be a historical fact that my husband served as president for eight years. And there's a lot that happened which helped the American people during those eight years. I want an economy that creates more jobs. And that's a lot of jobs. I want an economy that gets back to raising incomes for everybody. Most Americans haven't had a raise. I want an economy that's going to help lift millions of people out of poverty. Because, given the great recession, we have fallen back in the wrong direction. And I'm also going to be relying on President Obama. You know, I've already put him on notice. I'm going to be picking up the phone. I'm going to be calling and asking for his advice. And so we're going to put 'em all to work.

Scott Pelley: Senator, are you ready to be president of the United States?

Tim Kaine: I think I'm ready to lead. I'm ready first to be a supportive vice president so that the presidency of Hillary Clinton is a fantastic one. But if something were to put that in my path, as much as any human being would be ready, I'd be ready. And you gotta approach it with humility. But, you know what? You know, missionary, civil rights lawyer, local official, state official, federal official, like, I've climbed, and I haven't missed a rung on the ladder. And if it were to-- if it were to come that way, I could do it.

Hillary Clinton: We have our agenda. We have a very positive agenda. You'll hear a lot about it in Philadelphia this week. You know, people make fun of me sometimes because I do have plans. But I think I have this old-fashioned idea that when you are asking people to vote for you, it is kind of like a big job interview, and you oughta tell people what you think you can do for them. I think we can create more economic opportunity. I think we can improve education, make college affordable, deal with the myriad of issues that we confront.

Scott Pelley: But won't your hopes and dreams be dead on arrival at the Republican House of Representatives?

Hillary Clinton: I don't think so. And here's why. First of all, I know, and Tim knows, because we both have heard from many Republicans how distressed they are at the direction that Donald Trump is taking their party. I worked with Republicans. I came from Republican home. My father was a rock-ribbed Republican. I think the first Democrat he voted for was my husband, best I can remember. So we know that there are Republicans who share our concerns and want to be part of the solution, not just peddling fear and bigotry. And I also am hoping we will have a Democratic Senate, and we will make gains in the House. Who knows? Maybe we can take the House back. But we're going to come in with the attitude that, "You know what? We will talk, work and listen to you 24/7."

Scott Pelley: But wouldn't President Obama say exactly the same thing. And we've had eight years of gridlock. Not quite eight. But six years of gridlock.

Tim Kaine: Let me say, as a guy who's in the legislative branch right now, you said DOA, it's not DOA. And I think it's actually maybe gonna be easier than it's been in the past, a little bit. I do think we're gonna take a Senate majority for the Democrats.

Scott Pelley: In this election?

Tim Kaine: I do. I absolutely do. I think the House is going to remain in Republican hands. I think the margin will be narrowed. Some of the big things that we have to do: immigration reform, tax reform, mental health reform, criminal justice reform, they're only going to get done. I think they're only going to get done probably with a divided House scenario where each side's gotta give on something. Now here's the second thing. Some people don't agree with me on this. I was a brand new Senator in 2013. And the idiocy of Congress was to shut the government down for two weeks in October. And coming out of that, the pressure was put on the budget chair, Paul Ryan's shoulders and Patty Murray. Conservative Wisconsin Republican, progressive Washington Democrat, come up with a budget deal. Nobody thought they could. But I watched Patty Murray and Paul Ryan, who are principled people, cut a deal for the good of the country. I watched at the end of last year when Paul Ryan worked, and we got an appropriations bill that I thought was quite good. And when he went to the microphone to talk about that bill, here's what he said, "Democrats got some things that they liked, Republicans got some things they liked. We each had some things we didn't like." He could have said, "Hey, Republicans control both houses. We want it our way." But he didn't say that. He wants to do things. He wants not just a portrait but he would like a legacy. That's my belief. There's gonna be room to make some things happen.

Scott Pelley: Senator, in a sense, we're introducing you to 49 states. What hardship has formed your character?

Tim Kaine: In my public life, I've had some suffering. I was elected city councilman in 1994 in Richmond. We had the second highest homicide rate in the United States. And I just went to too many crime scenes. I went to police funerals. And there was a hopelessness about some of that. And I got to be governor. And the worst day of my life, and it will always be the worst day of my life, was the murder of these 32 beautiful young kids and these professors at Virginia Tech.

Scott Pelley: What did you do about it?

Tim Kaine: First, I did what I could personally, which was within 24 hours after that horrible shooting, I put a panel together of people who had no connection with Tech and no connection with the family. And I said, "I want you to tell me everything that went wrong and everything we can do to fix it." We improved mental health systems, though not enough. We-- There was a critical loop in the background record check system in Virginia. I was able to fix part of it of it executively. But when I went to my legislature even six months later and-- with the wound still fresh, I could not get the Virginia legislature to do the comprehensive background record check that we should do. And then I come into the Senate. We have that same battle within three months of being there, you know, after the horrible shooting at Sandy Hook right before I came into the Senate. You know, we had a vote on the Senate floor for common sense gun reform. The chamber was ringed with the family members from Sandy Hook, with Virginia Tech family members sitting with them and helping them. There's a phrase in the Letter to the Hebrews that says-- talks about being surrounded by a great cloud of witnesses. We were surrounded by a great cloud of witnesses, but we couldn't do the right thing.

Scott Pelley: And you thought what?

Tim Kaine: I just, you know, our public wants us to fix this. Gun owners want us to fix this. NRA members want us to fix this. And I thought how hard it is to do something that makes sense. So, you know, you mourn falling short, but we just gotta keep trying.

Scott Pelley: What can a president do about these terrible mass murders here and abroad that are now happening weekly in our world?

Hillary Clinton: Let's separate the mass murders that we have at places like Virginia Tech, Sandy Hook, Aurora, Colorado, and recognize that those are rooted in the much too readily available weapons of mass killings, mostly the assault weapons, and usually some kind of underlying motivation whether it is mental health or in the case of the killer in Charleston deep racist hatred. Those are homegrown. And they have to be addressed. And then we have people who claim to be and may well be inspired by if not directed by ISIS and they get radicalized. So I think number one we've got to have better gun safety rules, comprehensive background checks, closing the gun show loophole and the online loophole, changing the speed at which you get real time information, including mental health information to be part of that background check, and not selling the gun until the background check is completed, which was one of the problems in Charleston. For goodness sake, stopping terrorists, people on the watch list from being able to buy weapons. When it comes to terrorist killings, ISIS-inspired or other radical jihadist inspired, we need an intelligence surge. We have got to be much more connected from the local, to the state, to the national level with international sources of information.

Tim Kaine: And one other thing that's really important. As Secretary Clinton-- Hillary always says, you know, we gotta have a stronger world through stronger alliances. So when, you know, Donald Trump says, "Maybe we need to kinda pull our head back in our shell, and we don't need to have the alliances. Why do we need 'em? Why do we need to rely on 'em?" He's actually potentially cutting off exactly the kind of intelligence sharing that's going to be necessary to stop these kinda random attacks that do cause such terror. So these alliances matter. They're not, you know, they weren't about yesterday. They matter probably more today and tomorrow than they mattered yesterday.

In a moment, we ask Clinton and Kaine about the Republican attacks on her at their convention last week and about what it would mean to have a woman as president.

Part Two

At the Republican convention in Cleveland this past week, there were chants of "Lock her up" relating to Hillary Clinton's use of a private email server for official business when she was secretary of state.

The director of the FBI has said that Clinton was extremely careless and that in the tens of thousands of emails on the unsecured server several contained classified information. Donald Trump has used the email issue on many occasions to raise doubts about her character.

Scott Pelley: Madam Secretary, did you hear the Republican convention chanting, "Lock her up"?

Hillary Clinton: Well, I didn't hear it, because I wasn't watching. But I certainly heard about it, yes.

Scott Pelley: Did you feel threatened by that?

Hillary Clinton: No, I felt sad.

Scott Pelley: Sad?

Hillary Clinton: It felt very sad, Scott. I mean-- I don't know what their convention was about, other than criticizing me. I seem to be the only unifying theme that they had. There was no positive agenda. It was a very dark, divisive campaign. And the people who were speaking were painting a picture of our country that I did not recognize. You know, negative, scapegoating, fear, bigotry, smears. I just was so-- I was saddened by it.

Scott Pelley: He calls you "Crooked Hillary." What do you call him?

Hillary Clinton: I don't call him anything. And I'm not going to engage in that kind of insult fest that he seems to thrive on. So whatever he says about me, he's perfectly free to use up his own airtime and his own space to do. I'm going to talk about what he's done, how he has hurt people in business time after time after time. His vicious language against immigrants. His insulting a distinguished federal judge of Mexican heritage. His mocking a person with a disability. His really inflammatory language about Muslims, about American Muslims, about Muslims all over the world. His demeaning comments about women. I'm going to respond to what he has said that I think is so fundamentally at odds with who we are as a nation, where we need to be heading in the future, and the kind of dangerous, risky leadership that he's promising.

Tim Kaine: Can I say this? I don't want to-- she's done a good job of letting the, you know, water go off her back on this. That's not the way I feel. When I see this, you know, "Crooked Hillary," or I see the, "Lock her up," it's just ridiculous. It is ridiculous. The Republican FBI director makes a decision that there's nothing here that is, you know, warrants any additional activity. But oh--

Scott Pelley: Criminal prosecution.

Tim Kaine: Yeah, criminal but so the-- what, they're gonna say, "Well, we don't believe him now." You see, you saw all these folks trying to rehash the tragic deaths of Americans in Libya, which we should all feel for those families. They're trying to politicize it.

Scott Pelley: What's your responsibility for Benghazi? Did you make any mistakes around that?

Hillary Clinton: Well, Scott, there have been, I think now, nine separate investigations. And they did not find any such culpability. I took responsibility. I was Secretary of State. And I thought that was appropriate. And what I was determined to do is to find answers as to what actually happened, not what people claim, and what we could do to try to prevent that. That was in the tradition of what has happened in the past. We had horrible losses in Beirut when Ronald Reagan was president, and one of my favorite, former predecessors, George Shultz, was secretary of state, we had a Democratic Congress. They didn't politicize it. So when this happened in Benghazi, I immediately stood up an independent committee-- distinguished Americans, military and civilian experts. They came out and they said, "You know, the ball was dropped in security. And, you know, some of the decisions that were made probably should have been rethought."

Scott Pelley: But wasn't that your ball to carry?

Hillary Clinton: No, it wasn't. It was not my ball to carry. It was very-- be-- read the-- read the reports. Read all of the reports, all many hundreds of pages of them, including this latest one, which was a political exercise from the very beginning. Those never reached me. Those never came to my attention.

Scott Pelley: The concerns about the security never came to your attention. Didn't reach you.

Hillary Clinton: No, the experts-- we have security experts. I am not going to substitute my judgment for people who have been in the field, who understand what our men and women are up against. So this has all been investigated over and over again. But as Tim was just saying, it didn't get the result that some of the Republicans wanted, so they kept at it. And I feel very sorry that they have politicized it unlike any prior example. And I just think the most important challenge we face is learning from it and doing everything we can to keep our people safe.

Scott Pelley: I've got about three more questions that shouldn't take too long...one of them you might actually like.

Tim Kaine: One out of three...then we'll take one question.

Hillary Clinton: Yeah, exactly.

Scott Pelley: Alright. Do you think you blew it on the emails?

Hillary Clinton: Oh, I've said I did. Absolutely. I made a mistake. I should've had two accounts, one for personal and one for office. And I didn't, and I take responsibility for that.

Scott Pelley: Why did you do that? Have the private email servers?

Hillary Clinton: You know, Scott, other people did have-- other secretaries of state, other high-ranking members of administrations, plural-- and it was recommended that it would be convenient, and I thought it would be. It's turned out to be anything but.

Scott Pelley: Would there be a private email server in the White House?

Hillary Clinton: I'll tell ya one thing, that is one lesson I have learned the hard way, and there will not be any such thing in the White House. Although, I am quick to add, there's no evidence that it was ever hacked. And unfortunately, you can't say that for a lot of the government.

Scott Pelley: I was speaking to a young African-American man just the other day in a Democratic state. And he said, and I'll quote, "You know, I guess I would vote for Hillary except for that corruption problem," end quote. As I talked to him further, he didn't quite know what he meant by that. But that was his impression and concern. Why do you think people say that about you?

Hillary Clinton: Well first, I will take responsibility for any impression or anything I've ever done that people have legitimate questions about. But I think that it's fair to say there's been a concerted effort to convince people like that young man of something, nobody's quite sure what, but of something. I often feel like there's the Hillary standard and then there's the standard for everybody else. And--

Scott Pelley: What's the Hillary standard?

Hillary Clinton: Well, it-- it is-- you know, a lot of as you at the Republican convention-- unfounded, inaccurate, mean-spirited attacks with no basis in truth-- reality, which take on a life of their own. And for whatever reasons and I don't want to try to analyze the reasons. I see it. I understand it. People are very willing to say things about me, to make accusations about me that are-- I don't get upset about them anymore, but they are very regrettable.

Scott Pelley: Why do you put yourself through it?

Hillary Clinton: 'Cause I really believe in this country. And, boy, do I believe in it now more than ever after seeing what was presented last week. I believe that we are better than what we are hearing in the political discourse. I believe we can work together.

Scott Pelley: What do you care most about accomplishing as president?

Hillary Clinton: Well, I care most about getting the economy working for everybody. Not just those at the top. I care deeply about rebuilding the ladders of opportunity that have been battered, and broken, and knocked over, so that people can get an education that'll equip them for the future, that they can afford to go to college, that we can help them pay down their debt to get it off their backs. I care deeply about health care, something that has motivated me for many years. And how we defend the Affordable Care Act, fix it, make it work better, take on mental health, prescription drug costs, addiction that are just ripping the soul out of people, families, and communities. And I care deeply about the issues of race and discrimination, the kinds of systemic racism that we are still struggling with and that we have to deal with. And the whole suite of issues that I've talked about through this campaign, that I've worked on are ones that we're going to tackle from immigration reform to gun safety.

Scott Pelley: Who gets a tax increase? Who gets a tax cut?

Hillary Clinton: The middle class will not get a tax increase. That has been my pledge.

Scott Pelley: What does middle class mean?

Hillary Clinton: Well, we say below $250,000. Because here's what we want to do. We want to go where the money is. Most of the wealth increase, the increase in income, both active and passive, has gone to the very top of the income scale. So I'm with Warren Buffett, who says, "We need the Buffett rule." If you make a million dollars, you should pay a 30 percent rate because you should not be paying a lower rate than your secretary. We need a surcharge on incomes 5 million and up because I have said I will pay for everything I am proposing. I feel strongly about that. And it is in stark contrast to the terrible plans that Trump has been proposing which would soak the middle class, hurt working people, and give huge tax breaks to millionaires and billionaires.

Scott Pelley: Last one. What will be accomplished if you are elected the first woman president of the United States?

Hillary Clinton: I think it would be a great moment for our country because every little boy and every little girl should be given the chance to go as far as his or her hard work and talent might take them. I see it in the eyes of little girls who come to my events. They're so excited and they're so proud because maybe they just discovered we haven't had any girl presidents. And to accept that nomination on Thursday night, I'll be thinking about all the women who came before, all the women who went to Seneca Falls and, for the first time in history, talked about women's equality and women's rights, the suffragettes, the women who knocked their heads against all kinds of barriers and broke through in everything from, you know, space to politics. And I hope that it gives other women and girls the feeling that whatever their dreams might be, they can achieve them in this country.

Tim Kaine: And, you know, if you think about the history of our nation, we stated that all are equal, right, in 1776, but it took 144 years before we said, "And that means women can vote; not just men." So we said we were going to do one thing, but it took 144 years. And then it's taken--

Scott Pelley: Not to mention African Americans?

Tim Kaine: And we can march down the story the-- that that equality promise, which was like a North Star that we'll never reach, but we've been on a journey. And then it took another 100 years-- I mean, we're nearly 100 years later, in 2020, with no woman president. The next President of the United States will be the president that will celebrate 100 years of women having the right to vote. I mean, I think having a woman president lead that celebration would be, you know, one of these instances of history really working out right in a poetic and beautiful way. And part of this journey that we've been on, because then, we'll tackle the next imperfection we have. But this is something that is really, really exciting.