An unbowed Democratic leader Nancy Pelosi insisted on Thursday that she has the votes to become the next House speaker despite the emergence of a possible challenger who claimed party dissidents can block her historic bid.

In a flurry of one-on-one meetings, Pelosi courted wavering lawmakers, paying particular attention to the incoming, majority-making class of freshmen. She appeared to make headway as leaders of the Congressional Progressive Caucus described their session with her as a “productive and successful conversation” that they would share with their 70-plus membership.

The veteran Democratic leader is also relying on an aggressive outside campaign to lobby lawmakers, made up of liberal interest group leaders and high-profile Democrats, including one of former president Barack Obama’s closest advisers — former chief of staff Denis McDonough.

The powerful liberal organization, MoveOn, endorsed Pelosi while civil rights leader Rep. John Lewis (D-Ga.) said she has “demonstrated the proven, tested leadership we need to confront the issues before our nation.”

Pelosi remains short of the votes necessary, with solid opposition from at least 19 Democrats. Her first critical test is Nov. 28 in a secret-ballot contest among Democrats and then again in the higher-stakes public roll call of the entire House on Jan. 3.

Publicly, Pelosi has grown defiant, and annoyed, at questions about her hold on power. “I have overwhelming support in my caucus to be speaker of the House,” Pelosi told reporters at her weekly press briefing. “I happen to think at this point, I’m the best person for that.”

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Pelosi, already the first woman to serve as speaker, would be the first lawmaker to reclaim the gavel since 1955.

The anti-Pelosi faction received a potential lift Thursday when a veteran member of the Congressional Black Caucus said she would consider challenging Pelosi, helping rebut one of the central criticisms of this rump caucus of agitators: that they had no plan other than toppling Pelosi.

The CBC, which represents about 20 percent of the Democratic caucus, would likely be divided if Rep. Marcia L. Fudge (D-Ohio) follows through with the challenge. At least a dozen of its members have publicly endorsed Pelosi. Rep. James E. Clyburn (D-S.C.), a member of the CBC, said that his bid for majority whip, the No. 3 position, is a unified trifecta with Pelosi for speaker and Rep. Steny H. Hoyer (D-Md.) for majority leader.

“She would be a threat to me, as well,” Clyburn told reporters after a two-hour meeting of Democrats. “Because we put together a team, I’m supporting that team, and that team is Pelosi, Hoyer and Clyburn.”

But Rep. Cedric L. Richmond (D-La.) signaled Thursday that he is willing to consider Fudge.

“I’d probably be for it,” Richmond said, declining to suggest he would vote against Pelosi but in support of a friend. “Whatever Marcia does, I’m very pro-Marcia.”

When all the votes are tallied from last week’s midterm elections, Democrats will emerge with a likely majority of 15 to 17 votes. That gives Fudge and the other anti-Pelosi Democrats the rough estimate of how many Democrats they would need to deny her a majority in the January vote.

Outside advisers to Pelosi believe that the anti-Pelosi wing needs more than just the bare minimum of votes to prevent her from securing 218 votes, with the far greater threat coming from the freshman class that is dominated by female political stars. If many of them announced opposition to Pelosi, it could be a politically mortal wound.

In an interview with The Washington Post on Thursday, Fudge said she has been taken aback by the support from many of her colleagues for her possible bid.

“Over the last 12 hours, I’ve been overwhelmed by the amount of support I’ve received,” Fudge said, adding “probably closer to 30” Democrats have privately signaled they are willing to oppose Pelosi.

“Things could change rapidly,” she said.

Fudge, 66, a former CBC chair, said she is building a diverse coalition as she considers a run, talking with allies in the CBC, moderate Democrats and newly elected members.

In a significant boost for Pelosi on Thursday, Rep. Karen Bass (D-Calif.), a CBC member whom some have touted as a potential replacement for Pelosi, said in a tweet that she is backing Pelosi, 78, for the top leadership post.

Former attorney general Eric H. Holder Jr., who is contemplating a 2020 presidential bid, also voiced support for Pelosi, praising her in a tweet as “an architect of the recent midterm success.”

McDonough, Obama’s top aide in his second presidential term, has begun making calls to shore up support for Pelosi, according to an adviser.

The speaker’s vote used to be a perfunctory valedictory moment in which Republicans backed their nominee and Democrats their choice, the gavel going to whichever party had the majority.

But in this era of decentralized political forces, more rank-and-file feel free to oppose their party’s leader. These Democratic dissidents are following the footsteps of Republicans who chased one Republican speaker, John A. Boehner, out of office and made life difficult for House Speaker Paul D. Ryan (R-Wis.).

Pelosi could potentially draw votes from some moderate Republicans who have complained about how Boehner and Ryan ran the House.

“I’m open to crossing over,” Rep. Tom Reed (R-N.Y.) said. As chairman of the bipartisan Problem Solvers Caucus, Reed sits in a potential swing district and is working with moderate Democrats on ambitious rules changes.

But Pelosi, the leader of the Democratic caucus for almost 16 years, said she has no interest in getting a few extra votes from Republicans. “I intend to win the speakership with Democratic votes,” she said.

Pelosi has deputized the incoming chairman of the Rules Committee, Rep. Jim McGovern (D-Mass.), to try to produce a new rules package designed to open up the House so that more junior lawmakers can have input through their committees, an olive branch to the incoming freshmen and dozens of ambitious younger Democrats who have felt underutilized in recent years.

McGovern presented those proposals at a closed-door meeting Thursday afternoon but noted afterward that the process had just begun and he needed to hear from the nearly 60 incoming freshmen. “The new members just got here, so they haven’t had time to really have any input on any of this stuff,” he said.

Pelosi convened a meeting of her whip team for the race: 43 members met in her conference room just before noon Thursday in the Capitol, according to her allies.

There were signs some undecided Democrats would fall into line behind Pelosi.

Rashida Tlaib (D-Mich.), an incoming congresswoman who called for new leadership during her campaign, said she would meet with Pelosi on Friday to talk about committee assignments.

“We can celebrate that diversity, that rainbow of women coming in,” said Tlaib, who will be one of the first Muslim women in Congress. “But I think it’s really important that we also honor it by putting [women] on some really critical committees.”

Asked what she wants to hear from Pelosi, Tlaib said: “That working families are important and that me being here and celebrating that I’m a first is important but that she’ll honor it by putting me on critical committees where decisions are made.”

Robert Costa, Erica Werner and Elise Viebeck contributed to this report.