“As people walk away from Cawthorn, our job is to meet them,” she said, adding, “For those who don’t know what to make of a gay Christian minister, what is very clear with them is I’m being honest with them from the start.”

In Senator John Kennedy, Republican of Louisiana, Mr. Chambers does not have the villain that Democrats have made nationally of Ms. Greene. His campaign is based on his irreverent appeal — an outspoken Black progressive voice willing to smoke weed in a commercial, burn a Confederate flag and call white school board members racist to their faces for defending a school named after Robert E. Lee.

He raised $800,000 in the first three months of the year from 18,500 donors. The average contribution was $41, many of those small-dollar donors youthful and excited, the campaign said.

Critics say such campaigns are more about building the brand of Democratic consultants than making a play for a Senate seat. The man who created Mr. Chambers’s marijuana and Confederate flag ads, Erick Sanchez, helped run Andrew Yang’s presidential campaign and also hawks “Fouch on the Couch” throw pillows of Dr. Anthony Fauci for $40 a pop.

But Randy Jones, one of Mr. Chambers’s campaign chiefs, said the candidate should not be discounted. Mr. Chambers, he said, is taking a page from Ms. Abrams, who energized Georgia voters of color, urban liberals and the scatterings of rural Democrats to nearly win the governorship four years ago, build a political organization and set herself up for a rematch this year with the Republican governor, Brian Kemp.

Mr. Jones ran the campaign of another celebrity Democrat, Richard Ojeda of West Virginia, whose House campaign in 2018 was instructive in other ways. Mr. Ojeda, a trash-talking Bronze Star winner, sought to remake his party’s image in his emerging Republican stronghold as more muscular and more working class. He raised nearly $3 million, then lost by nearly 13 percentage points.