The victory of Kara Eastman over former Rep. Brad Ashford, the Democratic Party establishment’s favored candidate in a Nebraska primary Tuesday, has left the party at risk of being less competitive in a district that may be key to winning a majority in the House of Representatives in November.

Her upset win in an Omaha House district underscores the limits of often-cautious Democratic Party leaders’ influence in primary elections at a time when their voters and liberal grass-roots activists are hungry for a more confrontational approach.

Ms. Eastman, a 46-year-old nonprofit executive, campaigned on instituting a single-payer health-care system. In the wake of the Las Vegas shooting massacre last October, she told the Omaha World-Herald that Congress should consider a constitutional amendment “to define what bearing arms means” under the Second Amendment.

On Wednesday, Ms. Eastman said in an interview that she is for “common-sense gun-safety laws” including banning assault weapons and instituting background checks for new gun purchases. She said she didn’t recall proposing changing the Constitution to limit the Second Amendment.

“I’ve given a lot of interviews and I don’t remember that one,” she said.

Her bold positioning was a contrast to Mr. Ashford, a centrist who was on the Democratic Congressional Campaign Committee’s “Red-to-Blue” list of endorsed candidates. The DCCC has also been subsidizing two Nebraska Democratic Party staffers in a bid to boost voter turnout in the district.

What’s Dividing Democrats

Officials from both parties say Mr. Ashford’s defeat likely makes a Democratic victory in Nebraska against first-term GOP Rep. Don Bacon —who ousted Mr. Ashford in 2016—more difficult for Democrats.

“Kara Eastman is going to have to convince the voters that even though she may be more liberal than the district that it doesn’t really matter,” Mr. Ashford said. “What really matters is the inability of the Republican majority and the president to solve the problems that are affecting people.”

Mr. Ashford, who served a single term in Congress before losing a 2016 re-election bid to Mr. Bacon, said Wednesday that Democratic primary voters rejected his centrist message.

“If you’re mad about government, you can yell and scream but in the end we can fix it,” Mr. Ashford said. “That can only be done in the center. It can’t be done on the extremes.”

Republicans in Washington celebrated the Nebraska result. The National Republican Congressional Committee released polling showing Mr. Bacon with a 10-percentage point lead over Ms. Eastman. Mr. Bacon led Mr. Ashford by two points in a hypothetical matchup, the NRCC polls showed.

The DCCC hasn’t polled the Eastman-Bacon matchup, an official said.

Mr. Bacon said Wednesday it is “hard for me to say” whether Ms. Eastman’s primary victory makes his general election path easier.

“She’s too far to the left, but she’s going to bring some enthusiasm from her base” that Mr. Ashford wouldn’t, Mr. Bacon said.

Ms. Eastman rejected the idea that she is too liberal for the district.

“I’ve run on messages that I believe in and that I know represent the values of the people in the district,” she said. “The idea of providing health care for everybody, we can afford it. … And that’s what the people at the doors have told me they want.”

—Janet Hook contributed to this article.

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Democratic Voters Reject Establishment Choice in Nebraska, Clouding November Hopes