Pete Buttigieg wants to be president, a task almost as difficult as pronouncing his name (it's BOO'-tah-juhj). But the 37-year-old mayor of South Bend, Indiana and veteran of Afghanistan likes a tough project, in the right market. Like his 1905 home: "It was vacant. And the price was dropping a few thousand bucks every few weeks. And I realized it might actually dip to where I could afford it."

Buttigieg, lives there with his husband, Chasten. Now, he has his eyes on a different white house.

Once a long-shot, the mayor of Indiana's fourth-largest city has been rising in the polls, attracting contributions and attention.

The South Bend, Ind. mayor, Afghanistan veteran and Rhodes scholar, who's rising in the polls for the 2020 race, hopes to reanimate his party's values for a new era, including a connection with faith. CBS News

If elected, he says his top priority would be fixing the democratic system, from the electoral college to gerrymandering. Otherwise, he believes progress on climate change and healthcare would be difficult.

But what most people see in Pete Buttigieg is the man who would become America's youngest president.

CBS News' John Dickerson asked, "Do you think because Donald Trump has opened the window of possibilities that you actually benefit, in what's possible in a candidacy, in a presidency?

"In some ways, I mean, I never thought as a 37-year-old mayor that I would be able to say that I have more government experience than the President of the United States," he said.

CBS News' John Dickerson asked, "What other part of your life would you point people, who might be concerned given your age, who might say, 'Well, has he been tested?'"

Democratic presidential contender Pete Buttigieg, the mayor of South Bend, Ind., with CBS News' John Dickerson. CBS News

"Well, I remember one moment in Afghanistan, when I was responsible for making sure a vehicle I was driving got to where it was going safely," he said. "And you're warned that, for example, a magnetic IED could be placed on your vehicle. And once, it sounded to me as though somebody had attached something to the vehicle I was driving. And for a split second we had to figure out whether to ditch the vehicle, which would've been obviously very risky as well, because you're very obviously a target in the middle of a city where some people are pretty eager to attack you if you got the chance.

"Turned out what had happened was, that there was a beggar who had no legs. He was on sort of a dolly. And he would slap the side of the car in order to move himself along. If nothing else, it taught me not to overreact and not to panic when something's coming along that's pretty alarming."

Buttigieg is a trained pianist. He's also a Rhodes scholar from Harvard, and has studied the rise of another Democrat, also from Harvard, also a veteran, and also once considered "too young" for office: "If you look at his old campaign poster when he's running for Congress, it's this scrawny, toothy young guy, and the slogan is, 'The new generation offers a leader.'"

"Truman came out and said, 'Senator Kennedy, I'm sure you're gonna have a great future, but now is not your time,'" said Dickerson. The former president urged the young Senator to "be patient."

"Yeah, when you're young, you're always patted on the head and told that you're the future," Buttigieg replied. "But I'm interested in what you can bring to the present. And the present has always been shaped in some measure by young people.

Elected mayor of South Bend at age 29, Buttigieg took over just after Newsweek declared his hometown one of America's dying cities. Its Golden Age was more than 50 years ago, as home to the carmaker Studebaker. But in the early 1960s, Studebaker shut down, and took much of the town's economy along with it.

Part of the old Studebaker factory is now a tech center. Buttigieg calls it a symbol for what's happened in South Bend under his leadership – and what he'd do for the country as president.

During his campaign announcement on April 14, he said, "America deserves our optimism, deserves our courage, deserves our hope."

Dickerson asked, "You've talked about improving the symbolism of the presidency. Why is that important?"

"Because the presidency is also a moral office," Buttigieg replied. "It calls this nation to its highest values. And it sets the tone for the story that we tell ourselves. Narrative's a very powerful thing. And we need to make sure that everybody in America understands where they fit in this country's story."

But until recently, the mayor's own story was only half-told.

Dickerson asked, "When you went to serve [in Afghanistan], you wrote a letter in case you didn't come back. What's in the letter?"

"I wanted people who cared about me to know that I wouldn't have felt that I'd been cheated," he said. "That as tragic as it would be if my life were cut short, that it was so full that I wouldn't have left it with a sense of anger.

"But it's a strange thing to think about, too, because I didn't come out until after I came back. I also packed my bags for Afghanistan having no idea what it was like to be in love. And the richest and fullest part of my life is what happened after I came back and met Chasten and got married. So, thank God I came back."

Buttigieg came out publicly during his re-election bid in 2015. Last year he married junior-high teacher Chasten Glezman. Their two rescue dogs, Truman and one-eyed Buddy, have their own social media following.

Buddy interrupted Dickerson' interview with Pete and Chasten. "This is like politics," laughed Chasten. "This is like the trail. You think you're doing a great job and then someone comes from the left and interrupts everything."

"Or the right!"

"Welcome to politics! Oh, Buddy."

Pete and Chasten Buttigieg, with Buddy. CBS News

It's not the kind of marriage voters have seen before in a presidential campaign, and raises the question: Is the country ready for a gay president?

Dickerson asked, "Do you feel that your marriage is campaigning as well, because you are doing something that is new in American politics?"

"I think I'd argue I don't have to answer for it," Chasten replied. "I mean, we passed marriage equality. I don't think I have to answer for my marriage anymore."

Pete said, "I think, 'How could I possibly be doing this if it weren't for Chasten?' If I didn't have someone in my life who just cares about me as me?"

The messenger is the message: the youngest candidate is promising generational change with a campaign built on reanimating his party's values for a new era, including a connection with faith.

Dickerson asked Buttigieg if he has a particular favorite passage of scripture: "If there's one that I always try to think about when I'm deciding what to do, it's the Beatitudes," he said. "I also think about the scripture that says that when you pray, 'Be not like the hypocrites who love standing in the synagogues, in the corners of the streets, that they'll be seen by others and praised for it.' So, you know, there's a lot to turn to and a lot to check yourself in scripture."

And there may be a lot to check the political rise of Pete Buttigieg. But in the meantime, for those who have trouble with his name, he says call me Mayor Pete.



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Story produced by Dustin Stephens.