Londonderry, N.H. — There's a line that Pete Buttigieg, the youngest presidential candidate, employs in interviews and on the campaign trail to counter questions about his experience: "I've got more experience in government than the president, more executive experience than the vice president, and more military experience than anybody who's come into that office since George H.W. Bush."

It's that final point, in addition to his seven-month deployment to Afghanistan in 2014, that the 37-year-old mayor of South Bend, Indiana, hopes will appeal to military veterans in New Hampshire. Veterans comprise nearly 10 percent of the adult population in the state.

In his fifth trip to the first-in-the-nation primary state, the Harvard graduate and former Rhodes scholar stopped in Londonderry days before Memorial Day for a roundtable with veterans where he discussed attitudes toward former service members and reforms for the Department of Veterans Affairs (VA).

Pete Buttigieg seen May 20, 2019, in Miami, Florida. Getty

Reflecting on his return from Afghanistan, Buttigieg said the U.S. takes "seriously the mutual promise" it makes to veterans about their benefits and health care, but acknowledged the country has fallen short of fulfilling it.

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He suggested integrating civilian and VA care, but cautioned against privatizing the VA, arguing it would make the system "worse." The former Navy officer also proposed expanding resources to the VA and for Americans "to treat this less like a government operation" and instead have "a little more of customer service mentality."

"In other words, just because this isn't the private sector doesn't mean you shouldn't be treated the same way you would treat a customer that you want to take care of," Buttigieg said.

In a press gaggle after a town hall in Keene, New Hampshire, Buttigieg called for a broader cultural shift to address veterans' issues, instead of using members of the military as "props" for political gain.

"Some of these issues are a matter of policy," Buttigieg said. "But many of them are a matter of whether we are prepared to actually honor those who served, or whether we are going to continue down this path of them being used as props for the purposes of domestic political politics like we see in this administration."

Fred Walsh, 71, a retired sergeant in the U.S. Air Force, was crushed by a 750-pound tire from a B-52 bomber while serving overseas. A self-proclaimed "Biden-fan" who has not yet determined who he will vote for, Walsh said he is "tired of hearing these millennials say it's time for new blood," referencing leadership challenges to Speaker of the House Nancy Pelosi.

Still, the Vietnam vet said Buttigieg's candor appeals to him. "He gets right to the point and speaks to you from the heart. It's not just off a teleprompter," Walsh told CBS News in a phone call.

Buttigieg served in the Navy Reserve as an intelligence officer. Of the past four presidents, neither Trump, Obama or Clinton served, while President George W. Bush served in the Texas Air National Guard from 1968 to 1973.

Buttigieg is not the first veteran to showcase his military service record in the Granite State. Former Secretary of State John Kerry, who served as a lieutenant in the United States Navy during the Vietnam War, won the Democratic primary here in 2004. And the late Sen. John McCain toured VFW posts across the state, touting his military career en route to winning both the 2000 and 2008 Republican primaries.

After nearly 18 years of war, New Hampshire veterans told CBS News they are looking for a candidate willing to fight for the next generation of returning soldiers, regardless of party affiliation.

Bill Ryan, a Republican, served as a combat medic in Vietnam. The current commander of the New Hampshire chapter of the Veterans of Foreign Wars (VFW), Ryan says veterans in his state are protective of today's troops returning from overseas.

"We take it very personal when we see the way [Iraq and Afghanistan] veterans are treated," he told CBS News in a phone interview. "What politicians need to understand is that we're not going to let what happened to us when we returned happen to them."

Ryan served in Vietnam from 1965 to 1968, but said the VA diagnosed him with post-traumatic stress disorder and complications from exposure to Agent Orange just last year. "These kids deserve all kinds of benefits. They deserve better," he said.

Tammy Siekman, the chair of New Hampshire Democratic Caucus for Veterans and Military Families, helped arrange the veterans roundtable. "There's a lot of people who really just love [Buttigieg]," told CBS News. Her experience working with military veterans "is a lot more nonpartisan than I ever expected it to be," she said.

Jeremy Clemans, who attended a breakfast house party to hear Buttigieg speak Saturday, said Buttigieg's military service gives him the perspective to sacrifice military members and families make when called to serve. But Clemans, who has been to Sens. Kamala Harris and Cory Booker's events and is uncommitted to a candidate, said Buttigieg's military experience won't be the determining factor in who gets his vote.

"It is not a mandatory checkbox for me when I am looking at candidates," Clemans said.

Buttigieg has also used his military service record as a way to draw a contrast between himself and the current administration. In an interview with The Washington Post on Thursday, Buttigieg accused President Trump of using his "privileged status to fake a disability" to get draft deferments during the Vietnam War.

In the coming months, Buttigieg "will continue to hold events with Granite State veterans and our team will ramp up our efforts to mobilize and organize the strong support we've received from New Hampshire veterans," his campaign told CBS News.

Buttigieg is not the only young candidate with military experience. Fellow Democratic candidates Rep. Tulsi Gabbard of Hawaii and Rep. Seth Moulton of Massachusetts were deployed overseas, in the Marines and Army respectively.

Both are also making their pitches to New Hampshire veterans. Moulton held a veterans roundtable last weekend in Londonderry, while Gabbard spoke directly to veterans in Manchester at an opioid roundtable last month.