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.

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.

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“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 Mr. 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.

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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.