WASHINGTON — Somewhere on the road between here and Pennsylvania, the idea began to take root for Chrissy Houlahan: “I can’t not run.”

The daughter and granddaughter of Navy pilots, Ms. Houlahan had served 16 years as an Air Force engineer on active duty and in the Reserves. But in January, between conversations on a bus bound for the Women’s March and thoughts about her father, a Holocaust survivor rattled by the presidential election, she felt it was time to serve again.

In April, Ms. Houlahan, 50, who most recently worked as head of a nonprofit organization devoted to childhood literacy, entered the Democratic primary to challenge Representative Ryan A. Costello, a second-term Republican from the suburbs northwest of Philadelphia.

The Run-Up

The podcast that makes sense of the most delirious stretch of the 2016 campaign.

“I really do believe that we are in dangerous times,” she said.

Ms. Houlahan is among about 20 military veterans who have announced that they will run as Democrats for the House of Representatives next year. Democratic Party leaders are aggressively seeking former members of the military in hopes of increasing their appeal among the sort of frustrated voters who elected President Trump — and winning back the 24 seats they need to regain the Republican-controlled House.

In many cases, those veterans say they feel called to run for public office in response to Mr. Trump himself, whose policies they see as a threat to the country’s values and security.

Democratic officials also see candidates with a military pedigree as an appealing contrast to entrenched, career politicians. And they believe that candidates with military service help the party counter Republican claims that Democrats are weak on national security.

“If you look at the type of fear-mongering and scaremongering that Republicans do quite often when it comes to national security, quite unfairly, there is a strong patriotism that comes with being a veteran that makes those kinds of attacks fall flat and even backfire,” said John Lapp, who was the executive director of the Democratic Congressional Campaign Committee, the House Democrats’ campaign arm, in 2006, when his party took control of the House.

Mr. Trump has vigorously claimed that members of the military are among his strongest supporters, and they stood with him on Election Day: 60 percent of veterans voted for Mr. Trump, according to CNN’s exit polls. Earlier this year, Mr. Trump proposed increasing military spending by $54 billion, and last month, he signed legislation intended to improve accountability within the troubled Department of Veterans Affairs. This past weekend, Mr. Trump took a break from a trip to his golf club in Bedminster, N.J., to pay tribute to veterans, telling the crowd, “There is no place I would rather be than with you.”

But many of the veterans on next year’s Democratic ticket offer blunt criticism of the president, citing his willingness to dismiss allies and embrace adversaries. Some point to his decisions to weaken the State Department’s diplomatic capabilities, including by leaving many posts vacant more than five months after his inauguration. Active-duty service members, they say, often have to face the consequences of those decisions.

“That aggressive posture, whether toward allies or adversaries, puts the burden on service members,” Ms. Houlahan said.

Mikie Sherrill, a former Navy helicopter pilot running against Representative Rodney Frelinghuysen, a New Jersey Republican who presides over the powerful Appropriations Committee, mentioned in particular Mr. Trump’s refusal to recommit to the nation’s allies in NATO and his sharing of highly classified intelligence with Russia.

“Remarkable’s sort of putting it lightly. It’s a scary place to be,” she said. “I never would have imagined we would be here.”

In addition to the nearly 20 veterans who have announced they are running as Democrats in Republican-held House districts, about 15 more are expected to make announcements by the end of the summer, according to the Democratic Congressional Campaign Committee.

In many cases, they are political novices. Some went into careers in law after the military, others in business. Brendan Kelly, a former Navy officer who is expected to officially declare his candidacy for a seat in southwestern Illinois this week, is the top prosecutor in St. Clair County. Joseph Kopser, a former Army Ranger who served in Iraq and will challenge a longtime Republican incumbent in a deeply conservative Texas district, has started two businesses, including a transportation app he sold to Daimler A.G.

While some reached out to the party on their own, the campaign committee is focusing on courting those with military backgrounds. The Democrats forged an alliance earlier this year with VoteVets, a liberal political action committee that supports veterans running for Congress, and selected a former Marine Corps officer, Representative Seth Moulton of Massachusetts, to head up veteran recruitment.

With Mr. Trump’s approval ratings hovering around record lows for this point in a presidency, formidable candidates are lining up even in Republican strongholds. One of those is a southern chunk of North Carolina where Dan McCready, a Marine Corps veteran and businessman, hopes to be the first Democrat to win since the 1960s.

But the Democrats’ game plan to win back the House starts with targeting 23 Republican-held districts that Hillary Clinton won last fall.

With Election Day still 16 months away, Republicans say it is too early to compare Democratic recruitment with their own efforts. At least one veteran — Eddie Edwards, who served in the Navy and is challenging Representative Carol Shea-Porter, Democrat of New Hampshire — will run as a Republican. Most of the veterans serving in Congress are Republicans; of the 13 veterans in this year’s House freshman class, 10 are Republicans.

“Democrats have brutal primaries looming on the horizon,” Jesse Hunt, a spokesman for the National Republican Congressional Committee, said in an email. “Candidate biographies will matter less when the activist base pushes candidates further to the left with calls for single-payer health care and all-out obstruction to the Republican agenda.”

The current Democratic strategy, though, mirrors the one in 2006 that helped Democrats pick up 31 seats, their largest gain in more than three decades, and reclaim the House. Mayor Rahm Emanuel of Chicago, then an Illinois congressman and the chairman of the Democratic Congressional Campaign Committee, led an aggressive effort to target Republican districts and recruit candidates with résumés that bucked the stereotype of the liberal elite, like sheriffs, athletes and veterans.

More than a decade later, Democrats are still fighting that stereotype. Last month, conservative groups ran ads tying Representative Nancy Pelosi — the longtime House Democratic leader from San Francisco, often panned as the epitome of the “coastal elite” — to Jon Ossoff, the Democrat who ultimately lost a special election in the Atlanta suburbs.

Amid constant finger-pointing in Washington over putting party before country, several veterans said they believed their greatest asset was their demonstrated willingness to put others first.

“Officers eat last, after their men. That’s something that’s always stuck with me,” Mr. McCready said. “And I think that just captures what’s missing from Washington so much.”