With the national media descending on Georgia’s Sixth Congressional District, and outside money pouring in, the contest is viewed as a major test of whether a wave of left-wing activism since Mr. Trump’s inauguration will produce change at the ballot box.

Ms. Cox’s group is one of more than a dozen popping out like dogwood blooms in these comfortable suburbs of brick homes, shopping malls and technology companies. They have names like the Johns Creek-Milton Progressives Network, Roswell Resistance Huddle and Liberal Moms of Roswell and Cobb.

If a Democrat were to win the seat – once held by Newt Gingrich, and recently vacated by Tom Price, who joined Mr. Trump’s cabinet as secretary of health and human services — it would not be because of the $4 million that has come into the Ossoff campaign, much of it from national donors. Rather, it would be thanks to volunteer brigades roused by Mr. Trump’s election, who are knocking on doors, making phone calls and writing personalized post cards to turn out voters.

Even though the district favors Republicans, special elections are low-participation affairs; a strong ground game by Democrats could upend the usual outcome.

Mr. Ossoff, 30, a documentary filmmaker and first-time candidate, is hoping for a knockout punch in the open primary on April 18. All candidates in the race appear on the same ballot. If Mr. Ossoff, the polling leader, can win more than 50 percent, it will eliminate a runoff. If the race goes to a second round, scheduled June 20, a Republican would be favored because of the party’s historic advantage.