The hard-fought battle for Mr. Price’s seat in Atlanta’s northern reaches has not only become a financial arms race — by far the most expensive House contest in history — it has evolved into one of the most consequential special elections in decades.
Republicans, weighed down by Mr. Trump’s growing unpopularity, must demonstrate they can separate themselves from the president enough to hold suburban districts that only now are becoming battlegrounds.
And Democrats, facing a restive base hungry for victory after disappointing losses in Montana and Kansas, are under pressure to show they can notch something more than a moral victory in the sort of affluent seat they will need in order to take back the House majority.
An outright win in Georgia would serve as validation of the party’s overall strategy. Democrats have been recruiting aggressively in Republican-leaning seats — including in Michigan, Illinois and New Jersey — and party officials expect a wave of new challengers to announce their candidacies after the start of the next fund-raising quarter in July.
The stakes are highest for Republicans, who have held the district since the Carter administration without much of a challenge to speak of. Ms. Handel, the well-known former board chairwoman of the state’s most populous county, Fulton, and also a former Georgia secretary of state, is facing Jon Ossoff, a 30-year-old Democrat and former congressional aide who does not even live in the district.
“It’s a race that we have to win,” said Georgia State Senator Brandon Beach, a Republican whose district includes part of the terrain being fought on here.
Republican officials worry that if Mr. Ossoff wins, it would send a resounding statement about the intensity of the backlash to Mr. Trump, prompting incumbents to think twice about running for re-election, slowing fund-raising and, most significantly, further imperiling their already-stalemated legislative agenda.
“It’s not just symbolic — we really can’t afford to lose any seats at this point,” said Representative Tom Rooney, Republican of Florida, noting that “the factions” among congressional Republicans make their majorities more tenuous in practice than they may seem on paper.
In a district that was once nobody’s idea of “swing,” the parties themselves have elevated the stakes. The two candidates and outside groups have now spent more than $51 million.
Republican Party leaders thought having total control of Washington would end the gridlock of the Obama years. But with lawmakers unable to put a single piece of significant legislation on Mr. Trump’s desk and the president threatening the party with his unceasing Twitter eruptions and intervention in the investigation surrounding his campaign, Republicans fear that losing in Georgia may hasten the sort of every-man-for-himself acts of self-preservation that typically do not come this early in an election cycle.
And if vulnerable lawmakers turn inward, that could make passing controversial legislation, like an overhaul of the health care or tax system, even more difficult.
Such a vicious cycle, retrenchment ensuring inaction, could only further demoralize grass-roots Republicans, deteriorating the party’s standing even more. That malaise has already hobbled Republicans in Georgia, forcing national super PACs to spend heavily to aid Ms. Handel while Mr. Ossoff has raised over $24 million on his own, mainly with support from small donors.
“We actually have to have victories,” Mr. Rooney said.
Notably, Mr. Ossoff has made opposition to the American Health Care Act, the health care bill approved by House Republicans last month, a signature issue of his campaign. And while Mr. Ossoff has run on a centrist message over all, Democrats have run advertisements targeting liberal-leaning voters, especially African-Americans, with appeals to send a message to Mr. Trump: Republicans on Saturday circulated a picture of a truck parked in the district with a sign reading, “Hold Donald Trump Accountable, Vote Tuesday, June 20.”
“First and foremost, this is a referendum on the Trump presidency,” said Representative Tom Cole, Republican of Oklahoma. “The stakes here are not just for the House, the stakes are for the Trump presidency.”
In a briefing to House Republicans last week, Representative Steve Stivers of Ohio, the head of the House campaign arm, did not guarantee an election victory. “He said, ‘It’s going to be a late night,’” Mr. Cole recalled.
On the Democratic side, elected officials and party strategists say that Mr. Ossoff’s campaign has already served as a galvanizing force, spurring small donors into action and focusing the attention of voters and activists on the battle for the House. The notion that Mr. Price’s once-safe seat could be in play, strategists said, has helped encourage Democrats in other conservative-leaning seats.
Should Mr. Ossoff win, it could spur another wave of Democratic candidates to run in challenging districts.
Citing Georgia as a model, Andy Kim, a former national security official in the Obama administration, said he is likely to enter the race against Representative Tom MacArthur of New Jersey, who vaulted into the national spotlight as an architect of the House Republicans’ health care bill.
“We want that same energy,” Mr. Kim said. “We want people around the country to focus in and say: This is an opportunity for us to push back and hold MacArthur accountable for his actions.”
In Arizona, Randy Friese, a trauma surgeon turned state representative, said he has watched the Georgia race as he weighs a challenge to Senator Jeff Flake. Mr. Friese, who said he is leaning toward running, noted that Mr. Ossoff’s message — casting him largely as a nonpartisan candidate — had resonated with both Democrats and independent voters.
“Voters need people who have the political courage to stand up for their values and not just bend to the will of the party,” said Mr. Friese, who entered politics after treating Representative Gabrielle Giffords for a near-fatal gunshot wound in 2011.
Among the Democrats likely to announce campaigns in conservative-leaning districts, according to party strategists, are Matt Longjohn, a physician who is the Y.M.C.A.’s national health officer, against Representative Fred Upton of Michigan; Brendan Kelly, the St. Clair County, Ill., state’s attorney, against Representative Mike Bost; and Nancy Soderberg, a former ambassador, against Representative Ron DeSantis of Florida. Elissa Slotkin, a former Defense Department official, is moving toward a campaign against Representative Mike Bishop of Michigan.
All would be running in seats that tilt clearly toward the Republicans and where Democrats typically struggle to enlist strong candidates.
And in California, Gil Cisneros, a Navy veteran who won $266 million in the lottery, has been meeting with strategists about a challenge to Representative Ed Royce, according to Democrats familiar with his preparations. Mr. Royce has already drawn a promising Democratic opponent in Mai Khanh Tran, a pediatrician and former refugee.
Democratic officials argue that even a razor-thin defeat for Mr. Ossoff should be taken as an encouraging sign, but the party is under pressure to win. House Democrats only reluctantly, and minimally, competed in special elections earlier in the year in Kansas and Montana. But they poured millions into this race, even as Mr. Ossoff largely ran from the party’s agenda and leadership.
“My concern is that we might raise the bar too much, the expectations,” said Representative Michael E. Capuano, a Massachusetts Democrat. “Look guys, these are seats we shouldn’t even be playing in.”
Republicans are not even bothering to play down the consequences of losing.
“We all know this is a harbinger of national politics,” Mr. Perdue said, “and the world is looking, the nation is looking.”