Biden vs. Trump Live Updates: 2020 Election and Vice President Race

As an activist who jumped into the political arena after the police shooting of Michael Brown in Ferguson, Mo., six years ago, Cori Bush is accustomed to hard fights. She has been maced, shot at with rubber bullets and cloaked in tear gas at so many protests against police brutality that they have blurred together.

So when she heard that Representative William Lacy Clay, the 10-term Democrat she is challenging in Missouri’s Democratic primary on Tuesday, had called her “a prop” for the Justice Democrats, a national progressive group, Ms. Bush did not miss a beat.

“I had no title, no name, came out of the Ferguson uprising and people know who I am across the world,” Ms. Bush said on Saturday, responding to comments Mr. Clay made about her in an interview with The New York Times. “Not because I took money from some group — none of that. It is because I stayed true to a message of change for real people.”

Of Mr. Clay, she added, “He doesn’t understand that, because he doesn’t understand fighting for people.”

All over the country, progressive candidates like Ms. Bush, 44, are doing battle with veteran incumbents over the identity of the Democratic Party. In New York City, Jamaal Bowman defeated Representative Eliot L. Engel, a 16-term incumbent and powerful committee chairman. In western Massachusetts, Alex Morse, the mayor of Holyoke, is trying to unseat another long-serving chairman, Representative Richard E. Neal.

They are seeking to sustain the momentum gathered in 2018 by insurgents like Representative Alexandria Ocasio-Cortez. In St. Louis, Ms. Bush’s candidacy is a test of whether the national protest movement can translate into hard electoral power on the federal level.