Even those who back Ms. Bush expect many voters, and older black voters in particular, to support Mr. Clay.That has prompted Ms. Bush at times to tailor her message to a younger audience. When she filmed a radio ad last week, she had the producer underlay it with Cardi B’s “I Like It,” in part because she and her advisers thought it would help her appeal to young voters.

She was worried, however, about the optics of using a song with a Latin sound, because she said she had been accused of not caring enough about the black community.

“It’s almost like I should be solely focused on just issues that affect black people directly,” she said later. “We have to all work together.”

Despite the long odds Ms. Bush faces, there may be no better race to assess the actual power of an anti-establishment progressive message than here, where Mr. Clay, and his father before him, have held power for the last half-century.

Ms. Bush, for her part, remains undaunted, especially after seeing Ms. Ocasio-Cortez win.

“Before it was kind of like, ‘It is an uphill battle but you might be able to do it,’” she said. “Now, it’s like, ‘O.K., we think you’re going to do it.’”