Ms. Handel, 55, the runner-up in April at just under 20 percent, has bulked up her base, attracting supporters of other Republican candidates who were defeated in the first round. She now faces the risk of losing some voters because of Mr. Trump’s troubles.

Ms. Handel, however, has the advantage of being a known quantity to many voters, having cemented her conservative bona fides as a Fulton County commissioner and Georgia secretary of state long before Mr. Trump’s rise to power.

The challenge for Mr. Ossoff, a documentary filmmaker and former congressional staff member, will be turning out his anti-Trump coalition in equal force a second time during summer vacation season — while Ms. Handel hammers him for living outside the district and accuses him of exaggerating his credentials and being a puppet of liberal national Democrats.

Mr. Ossoff’s supporters are dishing it out, as well, with one frequent ad accusing Ms. Handel of profligate spending while secretary of state. At the same time, they are trying to change the basic math of the race by reaching out to millennials and to minorities, who are altering the flavor of what a generation ago was a classic swath of deeply conservative, white-flight suburbia.

Mr. Ossoff may receive some help from two recent developments that expanded access to the polls: the May 11 expansion of early voting sites in three Ossoff-friendly areas of DeKalb County, and a May 4 injunction by a federal judge that extended the voter registration period.

The expansion of the registration period was a result of a suit brought by the Lawyers’ Committee for Civil Rights Under Law. While the Georgia secretary of state’s office reports that at least 5,500 new registrations have been processed in the expanded period, it is not yet clear if it will benefit Democrats or Republicans, as Georgia voters do not list party affiliation on their registrations.