ATLANTA — When Jon Ossoff came within a couple of percentage points of winning 50 percent of the votes — and thus winning outright — in the special election in Georgia’s Sixth Congressional District on Tuesday, Democrats trumpeted the unexpectedly strong showing in a traditional Republican stronghold. But Republicans were also pleased that they had forced Mr. Ossoff into a June runoff against a seasoned candidate they believe their fractured party can unite behind.

This closely watched race in the suburbs north of Atlanta has been widely billed as a referendum on Donald J. Trump’s presidency, and local residents are girding themselves for a new bombardment of money and messaging as the two major parties fight for the chance to brand the Republican president as either damaged goods or a wily survivor.

Meanwhile, Mr. Trump, as divisive and catalyzing as ever, is waiting in the wings, amid speculation that he may be mulling a more personal involvement in the race that could end up stoking Republican excitement, Democratic anger — or both.

“I think we could be facing all-out war here for the next two months,” Kerwin Swint, a political science professor at Kennesaw State University in Kennesaw, Ga., said Wednesday.

Mr. Ossoff is a 30-year-old documentary filmmaker virtually no one had heard of until a few months ago. But he has become a sort of instant celebrity as liberals around the country sniffed weakness in a district that previously sent Newt Gingrich to Congress — but which Mr. Trump barely won in November.

Activists have filled Mr. Ossoff’s campaign chest with $8.3 million, and more is on the way: On Wednesday, Thomas E. Perez, the Democratic National Committee chairman, sent a fund-raising email encouraging party members to “go all-in and elect Jon,” and “send a big, loud message to Donald.”

Mr. Ossoff, one of 18 candidates on Tuesday’s ballot, received a little more than 48 percent of the vote. He will face the Republican Karen Handel in a June 20 runoff to fill the seat vacated by Tom Price, who is now Mr. Trump’s secretary of health and human services.

Ms. Handel, a former Georgia secretary of state, finished first among 11 Republican candidates on Tuesday night with just under 20 percent of the vote.

She has expressed support for Mr. Trump in the past, though not as fervently as some of the Republicans she bested on Tuesday. In a brief victory speech, she did not mention Mr. Trump at all.

But in an appearance Wednesday morning on CNN, Ms. Handel said she hoped Mr. Trump would come campaign for her. “It’s all hands on deck now,” she said. “There’s a lot at stake here.”

Mr. Trump is expected to be in the Atlanta area on April 28 to speak at a National Rifle Association event. It appears, from his Twitter account, that he has taken a keen interest in the race, and has offered his assistance: “Despite major outside money, FAKE media support and eleven Republican candidates, BIG ‘R’ win with runoff in Georgia,” he wrote Tuesday. “Glad to be of help!”

But even if he does not stump for Ms. Handel, his presence will be felt keenly in the runoff, with both candidates facing unique Trump-related dilemmas over the next few weeks.

If Ms. Handel keeps a cool distance from the president, she risks alienating the most fervent pro-Trump voters. If she embraces him, she may lend ammunition to Democrats eager to portray Ms. Handel as his tool.

Mr. Ossoff’s problem has to do with outrage. The anger over the Trump presidency has been the rocket fuel that has powered his surprisingly successful campaign, unleashing not only a flood of out-of-state donations, but a formidable army of canvassers and telephone-bank volunteers.

Whether that level of passion and involvement is sustainable remains to be seen. Democrats have a poor track record of turning up at midterm and special elections, and the June runoff comes during peak vacation season.

Alan Abramowitz, a political scientist at Emory University in Atlanta, believes that Mr. Ossoff’s supporters will remain motivated enough to return to the polls, and considers the race a “true tossup.” He noted that the conservative Tea Party movement, which bubbled up in early 2009, was still going strong enough to have a significant impact on the midterm elections in late 2010.

“The anti-Trump sentiment, we’ve seen that persist now since the election,” he said. “All the indications are that it is still present, and I don’t think it’s going to fade that quickly.”

Gina Rahman, 51, a mother, engineer and yoga instructor who has been volunteering for the Ossoff campaign since February, spoke this week as if she had no choice but to keep working through June. As she coordinated a pro-Ossoff sign-waving group in front of a polling place Tuesday in unincorporated East Cobb County, Ms. Rahman, an immigrant from Bangladesh, said she viewed Mr. Trump’s policies as a flirtation with “tribalism,” and spoke of him as a threat to the environment and the country’s democratic institutions.

“I ran a marathon,” she said, “and I’ll run a marathon again.”

Critics say Ms. Handel, 55, is somewhat short on charisma, and note that she lost recent bids for governor and United States senator. But she has a loyal base of support in the district, having served as chairwoman of the Fulton County Commission and chief executive of a local Chamber of Commerce.

In her campaign literature, she promotes her classic Republican stances: She is against abortion rights and for gun rights; advocates ending the Affordable Care Act and “birthright citizenship”; and boasts that she put in place a statewide photo ID system for voters “to ensure only qualified U.S. citizens, not illegal immigrants, are able to vote.”

She has criticized Mr. Ossoff — a champion of abortion rights and other liberal causes who has said he is not running a “partisan campaign” — as a “lightweight liberal.”

Charlie Harper, a longtime Georgia Republican operative and publisher of the political news site, said that Republicans who had voted for the other conservative candidates would naturally flock toward Ms. Handel, as would donors and prominent party members who were worried about playing favorites when so many Republicans were running.

“I think they’re going to be very comfortable with her,” Mr. Harper said. “Up until this point it really hasn’t been an even fight. Democrats had everything going for them. They essentially had one unified candidate.”

Joe Webb, 70, a Trump supporter and retired project manager from Marietta, spent Tuesday waving signs in the district for Bob Gray, a more overtly Trump-aligned Republican. He said he considered Ms. Handel to be a RINO — a Republican in Name Only — but said he would be voting for her to keep Mr. Ossoff out of Congress.

“I thought about it all day, licked my wounds and said, O.K., she’s got a fairly positive track record as a politician — she did get voter ID in the state of Georgia, which is a major accomplishment,” he said Wednesday.