Democrats scrambled to regroup on Wednesday after a disappointing special election defeat in Georgia, with lawmakers, activists and labor leaders speaking out in public and private to demand a more forceful economic message heading into the 2018 elections.

Among Democrats in Washington, the setback in Georgia revived or deepened a host of existing grievances about the party, accentuating tensions between moderate lawmakers and liberal activists and prompting some Democrats to question the leadership and political strategy of Nancy Pelosi, the House minority leader.

A small group of Democrats who have been critical of Ms. Pelosi in the past again pressed her to step down on Wednesday. And in a private meeting of Democratic lawmakers, Representative Tony Cárdenas of California, Ms. Pelosi’s home state, suggested the party should have a more open conversation about her effect on its political fortunes.

But the most acute and widely expressed concerns were economic. Speaking after a meeting of the Democratic caucus on Wednesday morning, Representative Hakeem Jeffries of New York said the party was preparing to be “aggressively focused on job creation and economic growth.” And Representative Jim Himes of Connecticut, who represents an affluent district near New York City, said Democrats must do more to compete with what he described as expansive and unrealistic promises by President Trump.

“It’s not enough to say, ‘I want jobs,’” Mr. Himes said. “You need more than that, particularly when you’re competing with a guy who is telling fantasies.”

Representative Debbie Dingell of Michigan called for Democrats to go “on offense” and attack the president’s perceived strength on economic matters with working-class voters.

“We need to show working men and women we understand their anxieties and fears,” she said, “and show that Trump is treating them like just another politician.”

By fiercely contesting a congressional race in the conservative Atlanta suburbs, Democrats had hoped to make an emphatic statement about the weakness of the Republican Party under Mr. Trump. Their candidate, Jon Ossoff, raised about $25 million, mostly in small donations, and assertively courted right-of-center voters with promises of economic development and fiscal restraint.

That vague message, Democrats said Wednesday, was plainly not powerful enough to counter an onslaught of Republican advertising that cast Mr. Ossoff as a puppet of liberal national Democrats, led by Ms. Pelosi, an intensely unpopular figure on the right and a longstanding target of Republican attacks. While Mr. Ossoff made inroads by exploiting Mr. Trump’s unpopularity and a backlash against health care legislation approved in the House, Democrats said they would have to do more to actually win.

Representative Eric Swalwell of California, who is close to party leaders, said Democrats would “crystallize our message on jobs, on health care” in the coming months. The results in Georgia and other special elections, he said, should encourage Democrats to campaign across a huge map of districts. “We need to compete everywhere,” he said.

Representative Ben Ray Luján of New Mexico, the chairman of the Democratic Congressional Campaign Committee, met Wednesday morning with a group of lawmakers who have been conferring about economic messaging, according to several people present who spoke on the condition of anonymity.

Mr. Luján told the group that his committee would examine the Georgia results for lessons, but he urged the lawmakers to portray the race in positive terms in their public comments, stressing that Democrats have consistently exceeded their historical performance in a series of special elections fought in solidly Republican territory.

It was in the meeting with Ms. Luján that Mr. Cárdenas, a member of the Democratic leadership, brought up Ms. Pelosi’s role in the Georgia race, calling it “the elephant in the room.” Ms. Pelosi was not present.

A spokeswoman for Mr. Cárdenas, while acknowledging his comment, said he had invoked the leader in the context of “what can be done to stand up to those attacks in the future.”

Ms. Pelosi has consistently rejected calls to step down, and there was little indication that her leadership post was at risk. She responded to the election results in a “Dear Colleague” letter to Democratic lawmakers late Wednesday, underscoring the party’s improving performance in conservative areas and saying that “every effort was made to win” in Georgia.

But Ms. Pelosi also said it was time for Democrats to “put forth our message,” and promised an economic one that “we can all embrace and utilize in our districts.”

She did not directly address the sometimes caustic criticism of her leadership from skeptics within the party. Several lawmakers who have opposed her in the past argued that Ms. Pelosi would undermine the party’s candidates for as long as she holds her post.

Representative Seth Moulton of Massachusetts, an open critic of Ms. Pelosi, called the Georgia result “frustrating” and urged a shake-up at the top of the party.

Representative Kathleen Rice of New York told CNN the entire Democratic leadership team should go.

Representative Tim Ryan of Ohio, who tried to unseat Ms. Pelosi as House minority leader late last fall, said she remained a political millstone for Democrats. But Mr. Ryan said the Democratic brand had also become “toxic” in much of the country because voters saw Democrats as “not being able to connect with the issues they care about.”

“Our brand is worse than Trump,” he said.

A top aide to Ms. Pelosi dismissed the idea that her lightning-rod status might have hurt the Democratic effort in Georgia, and pointed out that in some polls the Republican speaker, Paul D. Ryan, is viewed even more dismally.

Document | Memo From the Democratic Congressional Campaign Committee After the Democratic candidate lost in the special election for a House seat in Georgia on Tuesday, Representative Ben Ray Luján of New Mexico, the chairman of the Democratic Congressional Campaign Committee, tried to calm the Democratic Party with a memo that outlined in detail how Democrats aim to capture a majority in 2018.

Any Democratic leader would become a target for the right, said the aide, Drew Hammill, Ms. Pelosi’s deputy chief of staff.

“Republicans blew through millions to keep a ruby red seat and in their desperate rush to stop the hemorrhaging, they’ve returned to demonizing the party’s strongest fund-raiser and consensus builder,” he said. “They don’t have Clinton or Obama, so this is what they do.”

But in a possible omen, the first Democratic candidate to announce his campaign after the Georgia defeat immediately vowed not to support Ms. Pelosi for leader. Joe Cunningham, a South Carolina lawyer challenging Representative Mark Sanford, said Democrats needed “new leadership now.”

Even Democrats who are not openly antagonistic toward Ms. Pelosi acknowledged that a decade of Republican attacks had taken a toll: “It’s pretty difficult to undo the demonization of anyone,” said Representative Bill Pascrell Jr. of New Jersey.

In some respects, the sniping over the Democrats’ campaign message mirrors a larger divide in the Democratic Party, dating to the 2016 presidential primary contest and earlier. Senator Bernie Sanders of Vermont and his supporters have pressed Democrats to embrace a more bluntly populist message, assailing wealthy special interests and endorsing the expansion of social welfare programs, while more moderate Democrats in the party leadership have favored an approach closer to Mr. Ossoff’s.

But in four contested special elections in Republican districts — including two, in Kansas and Montana, featuring Sanders-style insurgents — neither method provided the party with a breakthrough victory.

In the absence of a smashing win that might have settled the left-versus-center debate, Democrats may face a longer process of internal deliberation before they settle on an approach that is broadly acceptable in the party.

Part of the Democrats’ challenge now is that the jobless rate is low, and many of the districts they are targeting are a lot like the Georgia seat: thriving suburbs filled with voters who have only watched their portfolios grow since Mr. Trump took office.

Even as they smarted from their defeat on Wednesday, Democrats signaled that they intend to compete across a vast area of the country in 2018. Mr. Luján, moving to calm the party, circulated a memo to lawmakers and staff members that declared there was “no doubt that Democrats can take back the House next fall” in the midterm elections. He wrote that six to eight dozen seats held by Republican lawmakers would be easier for Democrats to capture than Georgia’s Sixth.

Citing snippets of private polling, Mr. Luján said there were Republican seats in southern Arizona and Florida, northern New Jersey and the Kansas City, Kan., suburbs, where Democratic challengers were already ahead of Republican incumbents.

Democrats need to win 24 Republican-held seats to win control of the House.

On the Republican side, jubilation over the victory in Georgia mixed with lingering unease about the overall political environment. While Ms. Handel defeated Mr. Ossoff by about 10,000 votes and nearly four percentage points, Republican outside groups had to spend $18 million defending a district where the party’s candidates had won easily for decades.

And on the same night, a little-watched special election in South Carolina gave Republicans another scare, as an obscure Democrat, Archie Parnell, came within 3,000 votes of capturing a solidly Republican congressional district, with voter turnout far behind the Georgia race.

Nick Everhart, a Republican strategist in Ohio, said the party should not allow its relief at having kept Democrats at bay to turn into complacency. Up to this point, he said, Republicans have been beating Democrats only on solidly red turf.

“To pretend that there are not serious enthusiasm-gap issues with the G.O.P. base and, more crucially, independents fleeing, is missing the lessons that need to be learned before truly competitive seats are on the board,” Mr. Everhart said.

Still, the immediate aftermath of the Georgia election was plainly tougher on the Democratic side, as the party endured a fourth special election that ended with a better-than-usual showing by a defeated Democrat. That pattern may put Democrats on track to gain power in the 2018 elections, but 17 months is a long wait for a party so hungry to win.