Beatrice Torres is tired of voting for Grijalvas.

Year after year, Ms. Torres, 70, dutifully volunteered and cast her ballot for Representative Raúl M. Grijalva, a staunch Arizona progressive who was battling lung cancer when he was elected to his 12th term in November. He succumbed in March, the second of three House Democrats to die this year, bolstering the Republicans’ oh-so-slender majority.

Now, Mr. Grijalva’s oldest daughter, Adelita, has been asking Ms. Torres to vote for her in the Democratic primary on July 15, another Grijalva to take up her father’s seat. Several challengers are trying to block her, saying that Arizona needs a fresh voice and new ideas, not another Grijalva. And Ms. Torres agrees.

“Nobody is listening,” Ms. Torres said, clearly frustrated one scorching morning last week as she sat in her living room on Tucson’s working-class south side, shades drawn against the sun.

Ms. Grijalva is still likely to prevail in the heavily Democratic district — dozens of powerful Democrats have endorsed her, including the state’s two Democratic senators. But with two weeks to go, the special election in Arizona’s Seventh District is brewing into the next contest to question what the Democratic Party wants after its defeats of 2024 — experience versus generational change, left versus center, old versus new.

And beneath it all is simmering anger over the reluctance of former President Joseph R. Biden Jr. and other aging, ailing Democrats, like Mr. Grijalva, who died at 77, to leave office when their time had come.

“We need change,” Ms. Torres said.

Ms. Grijalva, 54, is a longtime elected official in Tucson, but to some frustrated voters, she is also the embodiment of their sclerotic party.